algebra.algebra.subalgebra.pointwise | 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

b2c707cd

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

93287238

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -71,7 +71,7 @@ theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring
     exact Submodule.mul_mem_mul (show (1 : A) ∈ S from one_mem S) (algebra_map_mem _ _)
   have := Submodule.mul_mem_mul hx hy
   rwa [mul_assoc, mul_comm _ T.to_submodule, ← mul_assoc _ _ S.to_submodule, mul_self,
-    mul_comm T.to_submodule, ← mul_assoc, mul_self] at this 
+    mul_comm T.to_submodule, ← mul_assoc, mul_self] at this
 #align subalgebra.mul_to_submodule Subalgebra.mul_toSubmodule
 -/

93287238

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 Weiser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.Algebra.Algebra.Operations
-import Mathbin.Algebra.Algebra.Subalgebra.Basic
-import Mathbin.RingTheory.Subring.Pointwise
-import Mathbin.RingTheory.Adjoin.Basic
+import Algebra.Algebra.Operations
+import Algebra.Algebra.Subalgebra.Basic
+import RingTheory.Subring.Pointwise
+import RingTheory.Adjoin.Basic
 
 #align_import algebra.algebra.subalgebra.pointwise from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"

93287238

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -85,7 +85,7 @@ protected def pointwiseMulAction : MulAction R' (Subalgebra R A)
     where
   smul a S := S.map (MulSemiringAction.toAlgHom _ _ a)
   one_smul S := (congr_arg (fun f => S.map f) (AlgHom.ext <| one_smul R')).trans S.map_id
-  mul_smul a₁ a₂ S :=
+  hMul_smul a₁ a₂ S :=
     (congr_arg (fun f => S.map f) (AlgHom.ext <| mul_smul _ _)).trans (S.map_map _ _).symm
 #align subalgebra.pointwise_mul_action Subalgebra.pointwiseMulAction
 -/

93287238

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 Weiser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.algebra.subalgebra.pointwise
-! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Operations
 import Mathbin.Algebra.Algebra.Subalgebra.Basic
 import Mathbin.RingTheory.Subring.Pointwise
 import Mathbin.RingTheory.Adjoin.Basic
 
+#align_import algebra.algebra.subalgebra.pointwise from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"
+
 /-!
 # Pointwise actions on subalgebras.

93287238

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -30,6 +30,7 @@ section Pointwise
 
 variable {R : Type _} {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
+#print Subalgebra.mul_toSubmodule_le /-
 theorem mul_toSubmodule_le (S T : Subalgebra R A) :
     S.toSubmodule * T.toSubmodule ≤ (S ⊔ T).toSubmodule :=
   by
@@ -38,7 +39,9 @@ theorem mul_toSubmodule_le (S T : Subalgebra R A) :
   show y * z ∈ S ⊔ T
   exact mul_mem (Algebra.mem_sup_left hy) (Algebra.mem_sup_right hz)
 #align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_le
+-/
 
+#print Subalgebra.mul_self /-
 /-- As submodules, subalgebras are idempotent. -/
 @[simp]
 theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubmodule :=
@@ -50,7 +53,9 @@ theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubm
     rw [← mul_one x]
     exact Submodule.mul_mem_mul hx1 (show (1 : A) ∈ S from one_mem S)
 #align subalgebra.mul_self Subalgebra.mul_self
+-/
 
+#print Subalgebra.mul_toSubmodule /-
 /-- When `A` is commutative, `subalgebra.mul_to_submodule_le` is strict. -/
 theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S T : Subalgebra R A) : S.toSubmodule * T.toSubmodule = (S ⊔ T).toSubmodule :=
@@ -71,9 +76,11 @@ theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring
   rwa [mul_assoc, mul_comm _ T.to_submodule, ← mul_assoc _ _ S.to_submodule, mul_self,
     mul_comm T.to_submodule, ← mul_assoc, mul_self] at this 
 #align subalgebra.mul_to_submodule Subalgebra.mul_toSubmodule
+-/
 
 variable {R' : Type _} [Semiring R'] [MulSemiringAction R' A] [SMulCommClass R' R A]
 
+#print Subalgebra.pointwiseMulAction /-
 /-- The action on a subalgebra corresponding to applying the action to every element.
 
 This is available as an instance in the `pointwise` locale. -/
@@ -84,38 +91,49 @@ protected def pointwiseMulAction : MulAction R' (Subalgebra R A)
   mul_smul a₁ a₂ S :=
     (congr_arg (fun f => S.map f) (AlgHom.ext <| mul_smul _ _)).trans (S.map_map _ _).symm
 #align subalgebra.pointwise_mul_action Subalgebra.pointwiseMulAction
+-/
 
 scoped[Pointwise] attribute [instance] Subalgebra.pointwiseMulAction
 
 open scoped Pointwise
 
+#print Subalgebra.coe_pointwise_smul /-
 @[simp]
 theorem coe_pointwise_smul (m : R') (S : Subalgebra R A) : ↑(m • S) = m • (S : Set A) :=
   rfl
 #align subalgebra.coe_pointwise_smul Subalgebra.coe_pointwise_smul
+-/
 
+#print Subalgebra.pointwise_smul_toSubsemiring /-
 @[simp]
 theorem pointwise_smul_toSubsemiring (m : R') (S : Subalgebra R A) :
     (m • S).toSubsemiring = m • S.toSubsemiring :=
   rfl
 #align subalgebra.pointwise_smul_to_subsemiring Subalgebra.pointwise_smul_toSubsemiring
+-/
 
+#print Subalgebra.pointwise_smul_toSubmodule /-
 @[simp]
 theorem pointwise_smul_toSubmodule (m : R') (S : Subalgebra R A) :
     (m • S).toSubmodule = m • S.toSubmodule :=
   rfl
 #align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmodule
+-/
 
+#print Subalgebra.pointwise_smul_toSubring /-
 @[simp]
 theorem pointwise_smul_toSubring {R' R A : Type _} [Semiring R'] [CommRing R] [Ring A]
     [MulSemiringAction R' A] [Algebra R A] [SMulCommClass R' R A] (m : R') (S : Subalgebra R A) :
     (m • S).toSubring = m • S.toSubring :=
   rfl
 #align subalgebra.pointwise_smul_to_subring Subalgebra.pointwise_smul_toSubring
+-/
 
+#print Subalgebra.smul_mem_pointwise_smul /-
 theorem smul_mem_pointwise_smul (m : R') (r : A) (S : Subalgebra R A) : r ∈ S → m • r ∈ m • S :=
   (Set.smul_mem_smul_set : _ → _ ∈ m • (S : Set A))
 #align subalgebra.smul_mem_pointwise_smul Subalgebra.smul_mem_pointwise_smul
+-/
 
 end Pointwise

93287238

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -69,7 +69,7 @@ theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring
     exact Submodule.mul_mem_mul (show (1 : A) ∈ S from one_mem S) (algebra_map_mem _ _)
   have := Submodule.mul_mem_mul hx hy
   rwa [mul_assoc, mul_comm _ T.to_submodule, ← mul_assoc _ _ S.to_submodule, mul_self,
-    mul_comm T.to_submodule, ← mul_assoc, mul_self] at this
+    mul_comm T.to_submodule, ← mul_assoc, mul_self] at this 
 #align subalgebra.mul_to_submodule Subalgebra.mul_toSubmodule
 
 variable {R' : Type _} [Semiring R'] [MulSemiringAction R' A] [SMulCommClass R' R A]

93287238

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -87,7 +87,7 @@ protected def pointwiseMulAction : MulAction R' (Subalgebra R A)
 
 scoped[Pointwise] attribute [instance] Subalgebra.pointwiseMulAction
 
-open Pointwise
+open scoped Pointwise
 
 @[simp]
 theorem coe_pointwise_smul (m : R') (S : Subalgebra R A) : ↑(m • S) = m • (S : Set A) :=

93287238

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -30,9 +30,6 @@ section Pointwise
 
 variable {R : Type _} {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
-/- warning: subalgebra.mul_to_submodule_le -> Subalgebra.mul_toSubmodule_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_leₓ'. -/
 theorem mul_toSubmodule_le (S T : Subalgebra R A) :
     S.toSubmodule * T.toSubmodule ≤ (S ⊔ T).toSubmodule :=
   by
@@ -42,9 +39,6 @@ theorem mul_toSubmodule_le (S T : Subalgebra R A) :
   exact mul_mem (Algebra.mem_sup_left hy) (Algebra.mem_sup_right hz)
 #align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_le
 
-/- warning: subalgebra.mul_self -> Subalgebra.mul_self is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.mul_self Subalgebra.mul_selfₓ'. -/
 /-- As submodules, subalgebras are idempotent. -/
 @[simp]
 theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubmodule :=
@@ -57,9 +51,6 @@ theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubm
     exact Submodule.mul_mem_mul hx1 (show (1 : A) ∈ S from one_mem S)
 #align subalgebra.mul_self Subalgebra.mul_self
 
-/- warning: subalgebra.mul_to_submodule -> Subalgebra.mul_toSubmodule is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule Subalgebra.mul_toSubmoduleₓ'. -/
 /-- When `A` is commutative, `subalgebra.mul_to_submodule_le` is strict. -/
 theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S T : Subalgebra R A) : S.toSubmodule * T.toSubmodule = (S ⊔ T).toSubmodule :=
@@ -83,12 +74,6 @@ theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring
 
 variable {R' : Type _} [Semiring R'] [MulSemiringAction R' A] [SMulCommClass R' R A]
 
-/- warning: subalgebra.pointwise_mul_action -> Subalgebra.pointwiseMulAction is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))], MulAction.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4))
-but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toSMul.{u3, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)], MulAction.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4))
-Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_mul_action Subalgebra.pointwiseMulActionₓ'. -/
 /-- The action on a subalgebra corresponding to applying the action to every element.
 
 This is available as an instance in the `pointwise` locale. -/
@@ -104,44 +89,23 @@ scoped[Pointwise] attribute [instance] Subalgebra.pointwiseMulAction
 
 open Pointwise
 
-/- warning: subalgebra.coe_pointwise_smul -> Subalgebra.coe_pointwise_smul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' 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 @[simp]
 theorem coe_pointwise_smul (m : R') (S : Subalgebra R A) : ↑(m • S) = m • (S : Set A) :=
   rfl
 #align subalgebra.coe_pointwise_smul Subalgebra.coe_pointwise_smul
 
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 @[simp]
 theorem pointwise_smul_toSubsemiring (m : R') (S : Subalgebra R A) :
     (m • S).toSubsemiring = m • S.toSubsemiring :=
   rfl
 #align subalgebra.pointwise_smul_to_subsemiring Subalgebra.pointwise_smul_toSubsemiring
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmoduleₓ'. -/
 @[simp]
 theorem pointwise_smul_toSubmodule (m : R') (S : Subalgebra R A) :
     (m • S).toSubmodule = m • S.toSubmodule :=
   rfl
 #align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmodule
 
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-  forall {R' : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} [_inst_7 : Semiring.{u1} R'] [_inst_8 : CommRing.{u2} R] [_inst_9 : Ring.{u3} A] [_inst_10 : MulSemiringAction.{u1, u3} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_7)) (Ring.toSemiring.{u3} A _inst_9)] [_inst_11 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u3} A _inst_9)] [_inst_12 : SMulCommClass.{u1, u2, u3} R' R A (SMulZeroClass.toHasSmul.{u1, u3} R' A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_9))))))) (DistribSMul.toSmulZeroClass.{u1, u3} R' A (AddMonoid.toAddZeroClass.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_9)))))) (DistribMulAction.toDistribSMul.{u1, u3} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_7)) (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_9))))) (MulSemiringAction.toDistribMulAction.{u1, u3} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_7)) (Ring.toSemiring.{u3} A _inst_9) _inst_10)))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_9))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_8)))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_9))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_8))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_9))))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_8)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (Ring.toSemiring.{u3} A _inst_9)))) (Algebra.toModule.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u3} A _inst_9) _inst_11)))))] (m : R') (S : Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u3} A _inst_9) _inst_11), Eq.{succ u3} (Subring.{u3} A _inst_9) (Subalgebra.toSubring.{u2, u3} R A _inst_8 _inst_9 _inst_11 (SMul.smul.{u1, u3} R' (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u3} A _inst_9) _inst_11) (MulAction.toHasSmul.{u1, u3} R' (Subalgebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u3} A _inst_9) _inst_11) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_7)) (Subalgebra.pointwiseMulAction.{u2, u3, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u3} A _inst_9) _inst_11 R' _inst_7 _inst_10 _inst_12)) m S)) (SMul.smul.{u1, u3} R' (Subring.{u3} A _inst_9) (MulAction.toHasSmul.{u1, u3} R' (Subring.{u3} A _inst_9) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_7)) (Subring.pointwiseMulAction.{u1, u3} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_7)) _inst_9 _inst_10)) m (Subalgebra.toSubring.{u2, u3} R A _inst_8 _inst_9 _inst_11 S))
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-Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_smul_to_subring Subalgebra.pointwise_smul_toSubringₓ'. -/
 @[simp]
 theorem pointwise_smul_toSubring {R' R A : Type _} [Semiring R'] [CommRing R] [Ring A]
     [MulSemiringAction R' A] [Algebra R A] [SMulCommClass R' R A] (m : R') (S : Subalgebra R A) :
@@ -149,12 +113,6 @@ theorem pointwise_smul_toSubring {R' R A : Type _} [Semiring R'] [CommRing R] [R
   rfl
 #align subalgebra.pointwise_smul_to_subring Subalgebra.pointwise_smul_toSubring
 
-/- warning: subalgebra.smul_mem_pointwise_smul -> Subalgebra.smul_mem_pointwise_smul is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align subalgebra.smul_mem_pointwise_smul Subalgebra.smul_mem_pointwise_smulₓ'. -/
 theorem smul_mem_pointwise_smul (m : R') (r : A) (S : Subalgebra R A) : r ∈ S → m • r ∈ m • S :=
   (Set.smul_mem_smul_set : _ → _ ∈ m • (S : Set A))
 #align subalgebra.smul_mem_pointwise_smul Subalgebra.smul_mem_pointwise_smul

93287238

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -31,10 +31,7 @@ section Pointwise
 variable {R : Type _} {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
 /- warning: subalgebra.mul_to_submodule_le -> Subalgebra.mul_toSubmodule_le is a dubious translation:
-lean 3 declaration is
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(Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A 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(CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) S T))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_leₓ'. -/
 theorem mul_toSubmodule_le (S T : Subalgebra R A) :
     S.toSubmodule * T.toSubmodule ≤ (S ⊔ T).toSubmodule :=
@@ -46,10 +43,7 @@ theorem mul_toSubmodule_le (S T : Subalgebra R A) :
 #align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_le
 
 /- warning: subalgebra.mul_self -> Subalgebra.mul_self is a dubious translation:
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x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A 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+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_self Subalgebra.mul_selfₓ'. -/
 /-- As submodules, subalgebras are idempotent. -/
 @[simp]
@@ -64,10 +58,7 @@ theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubm
 #align subalgebra.mul_self Subalgebra.mul_self
 
 /- warning: subalgebra.mul_to_submodule -> Subalgebra.mul_toSubmodule is a dubious translation:
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_inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) S) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} 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x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A 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(CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))) S T))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule Subalgebra.mul_toSubmoduleₓ'. -/
 /-- When `A` is commutative, `subalgebra.mul_to_submodule_le` is strict. -/
 theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
@@ -137,10 +128,7 @@ theorem pointwise_smul_toSubsemiring (m : R') (S : Subalgebra R A) :
 #align subalgebra.pointwise_smul_to_subsemiring Subalgebra.pointwise_smul_toSubsemiring
 
 /- warning: subalgebra.pointwise_smul_to_submodule -> Subalgebra.pointwise_smul_toSubmodule is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u3, u2} R A _inst_1 _inst_2 _inst_3) S))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmoduleₓ'. -/
 @[simp]
 theorem pointwise_smul_toSubmodule (m : R') (S : Subalgebra R A) :

93287238

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -34,7 +34,7 @@ variable {R : Type _} {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} 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_inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), LE.le.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (OmegaCompletePartialOrder.toPartialOrder.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) T) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.mul.{u2, u1} R _inst_1 A _inst_2 _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) 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(PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A 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_inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) S T))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), LE.le.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (OmegaCompletePartialOrder.toPartialOrder.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) T) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.mul.{u2, u1} R _inst_1 A _inst_2 _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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(CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) S T))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_leₓ'. -/
 theorem mul_toSubmodule_le (S T : Subalgebra R A) :
     S.toSubmodule * T.toSubmodule ≤ (S ⊔ T).toSubmodule :=
@@ -49,7 +49,7 @@ theorem mul_toSubmodule_le (S T : Subalgebra R A) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} 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_inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.mul.{u2, u1} R _inst_1 A _inst_2 _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A 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Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} 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_inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S)
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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_inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_self Subalgebra.mul_selfₓ'. -/
 /-- As submodules, subalgebras are idempotent. -/
 @[simp]
@@ -67,7 +67,7 @@ theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubm
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_4 : CommSemiring.{u1} R] [_inst_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5)] (S : Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (T : Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.mul.{u1, u2} R _inst_4 A (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A 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_inst_6))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) => (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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(CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) => (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : CommSemiring.{u2} R] [_inst_5 : CommSemiring.{u1} A] [_inst_6 : Algebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5)] (S : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (T : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) T) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (Submodule.mul.{u2, u1} R _inst_4 A (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))))) (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (fun (_x : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))))) (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) 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(Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))) S T))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : CommSemiring.{u2} R] [_inst_5 : CommSemiring.{u1} A] [_inst_6 : Algebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5)] (S : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (T : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) T) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (Submodule.mul.{u2, u1} R _inst_4 A (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))))) (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (fun (_x : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))))) (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))) S T))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule Subalgebra.mul_toSubmoduleₓ'. -/
 /-- When `A` is commutative, `subalgebra.mul_to_submodule_le` is strict. -/
 theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
@@ -140,7 +140,7 @@ theorem pointwise_smul_toSubsemiring (m : R') (S : Subalgebra R A) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))] (m : R') (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u3, u2} R A _inst_1 _inst_2] {R' : Type.{u1}} [_inst_4 : Semiring.{u1} R'] [_inst_5 : MulSemiringAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u1, u3, u2} R' R A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_2 _inst_3)] (m : R') (S : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u3, u2} R A _inst_1 _inst_2 _inst_3) S))
+  forall {R : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u3, u2} R A _inst_1 _inst_2] {R' : Type.{u1}} [_inst_4 : Semiring.{u1} R'] [_inst_5 : MulSemiringAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u1, u3, u2} R' R A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_2 _inst_3)] (m : R') (S : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} 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_inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (Subalgebra.toSubmodule.{u3, u2} R A _inst_1 _inst_2 _inst_3) S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmoduleₓ'. -/
 @[simp]
 theorem pointwise_smul_toSubmodule (m : R') (S : Subalgebra R A) :

93287238

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -32,7 +32,7 @@ variable {R : Type _} {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
 /- warning: subalgebra.mul_to_submodule_le -> Subalgebra.mul_toSubmodule_le is a dubious translation:
 lean 3 declaration is
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} 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_inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T))
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), LE.le.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (OmegaCompletePartialOrder.toPartialOrder.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) T) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.mul.{u2, u1} R _inst_1 A _inst_2 _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, 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(Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) S T))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_leₓ'. -/
@@ -47,7 +47,7 @@ theorem mul_toSubmodule_le (S T : Subalgebra R A) :
 
 /- warning: subalgebra.mul_self -> Subalgebra.mul_self is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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_inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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 but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) 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(Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R 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_inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_self Subalgebra.mul_selfₓ'. -/
@@ -65,7 +65,7 @@ theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubm
 
 /- warning: subalgebra.mul_to_submodule -> Subalgebra.mul_toSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_4 : CommSemiring.{u1} R] [_inst_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5)] (S : Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (T : Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) 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(Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) S T))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_4 : CommSemiring.{u1} R] [_inst_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5)] (S : Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (T : Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.mul.{u1, u2} R _inst_4 A (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) => (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 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(PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) S T))
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : CommSemiring.{u2} R] [_inst_5 : CommSemiring.{u1} A] [_inst_6 : Algebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5)] (S : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (T : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) T) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (Submodule.mul.{u2, u1} R _inst_4 A (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))))) (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (fun (_x : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))))) (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun 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_inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))) S T))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule Subalgebra.mul_toSubmoduleₓ'. -/
@@ -138,7 +138,7 @@ theorem pointwise_smul_toSubsemiring (m : R') (S : Subalgebra R A) :
 
 /- warning: subalgebra.pointwise_smul_to_submodule -> Subalgebra.pointwise_smul_toSubmodule is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))] (m : R') (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) 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_inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, 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_inst_3) (MulAction.toHasSmul.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u1, u2, u3} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6)) m S)) (SMul.smul.{u3, u2} R' (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SMulZeroClass.toHasSmul.{u3, u2} R' (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddZeroClass.toHasZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoid.toAddZeroClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoid.toAddZeroClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (DistribMulAction.toDistribSMul.{u3, u2} R' (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.pointwiseDistribMulAction.{u3, u1, u2} R' R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5) _inst_6)))) m (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))] (m : R') (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 but is expected to have type
   forall {R : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u3, u2} R A _inst_1 _inst_2] {R' : Type.{u1}} [_inst_4 : Semiring.{u1} R'] [_inst_5 : MulSemiringAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u1, u3, u2} R' R A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_2 _inst_3)] (m : R') (S : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S)) (FunLike.coe.{succ u2, succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u2, u2, u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u3, u2} R A _inst_1 _inst_2 _inst_3) S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmoduleₓ'. -/

93287238

bump to nightly-2023-04-20-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

fbfe5c3e

Diff

@@ -34,7 +34,7 @@ variable {R : Type _} {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} 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_inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), LE.le.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (OmegaCompletePartialOrder.toPartialOrder.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) T) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.mul.{u2, u1} R _inst_1 A _inst_2 _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) 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Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) S T))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), LE.le.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) 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(Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) S T))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_leₓ'. -/
 theorem mul_toSubmodule_le (S T : Subalgebra R A) :
     S.toSubmodule * T.toSubmodule ≤ (S ⊔ T).toSubmodule :=
@@ -49,7 +49,7 @@ theorem mul_toSubmodule_le (S T : Subalgebra R A) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) 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(Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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_inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun 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Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S)
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.mul.{u2, u1} R _inst_1 A _inst_2 _inst_3)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) 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_inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A 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(CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))))) (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3) S)
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_self Subalgebra.mul_selfₓ'. -/
 /-- As submodules, subalgebras are idempotent. -/
 @[simp]
@@ -67,7 +67,7 @@ theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubm
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_4 : CommSemiring.{u1} R] [_inst_5 : CommSemiring.{u2} A] [_inst_6 : Algebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5)] (S : Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (T : Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) 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_inst_6) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) T)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) => (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) A (Subalgebra.setLike.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) S T))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : CommSemiring.{u2} R] [_inst_5 : CommSemiring.{u1} A] [_inst_6 : Algebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5)] (S : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (T : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A 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(CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) T)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))) (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (fun (_x : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A 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(CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) (RelEmbedding.toEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))) S T))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : CommSemiring.{u2} R] [_inst_5 : CommSemiring.{u1} A] [_inst_6 : Algebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5)] (S : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (T : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6), Eq.{succ u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) T) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (Submodule.mul.{u2, u1} R _inst_4 A (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) 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_inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) S) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))))) (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))) S T))
 Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule Subalgebra.mul_toSubmoduleₓ'. -/
 /-- When `A` is commutative, `subalgebra.mul_to_submodule_le` is strict. -/
 theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
@@ -140,7 +140,7 @@ theorem pointwise_smul_toSubsemiring (m : R') (S : Subalgebra R A) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))] (m : R') (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u3, u2} R A _inst_1 _inst_2] {R' : Type.{u1}} [_inst_4 : Semiring.{u1} R'] [_inst_5 : MulSemiringAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u1, u3, u2} R' R A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_2 _inst_3)] (m : R') (S : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S)) (HSMul.hSMul.{u1, u2, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (instHSMul.{u1, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (SMulZeroClass.toSMul.{u1, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (IdemSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.idemSemiring.{u3, u2} R _inst_1 A _inst_2 _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddMonoidWithOne.toAddMonoid.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (IdemSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.idemSemiring.{u3, u2} R _inst_1 A _inst_2 _inst_3))))))) (DistribMulAction.toDistribSMul.{u1, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (IdemSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.idemSemiring.{u3, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.pointwiseDistribMulAction.{u1, u3, u2} R' R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5) _inst_6))))) m (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S))
+  forall {R : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u3, u2} R A _inst_1 _inst_2] {R' : Type.{u1}} [_inst_4 : Semiring.{u1} R'] [_inst_5 : MulSemiringAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u1, u3, u2} R' R A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_2 _inst_3)] (m : R') (S : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (Subalgebra.toSubmodule.{u3, u2} R A _inst_1 _inst_2 _inst_3) S))
 Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmoduleₓ'. -/
 @[simp]
 theorem pointwise_smul_toSubmodule (m : R') (S : Subalgebra R A) :

93287238

bump to nightly-2023-03-19-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1f4705ccdfe1e557fc54a0ce081a05e33d2e6240

b19efad4

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 
 ! This file was ported from Lean 3 source module algebra.algebra.subalgebra.pointwise
-! leanprover-community/mathlib commit b2c707cd190a58ea0565c86695a19e99ccecc215
+! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.RingTheory.Adjoin.Basic
 /-!
 # Pointwise actions on subalgebras.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 If `R'` acts on an `R`-algebra `A` (so that `R'` and `R` actions commute)
 then we get an `R'` action on the collection of `R`-subalgebras.
 -/

b2c707cd

bump to nightly-2023-03-16-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

bef0d6af

Diff

@@ -27,6 +27,12 @@ section Pointwise
 
 variable {R : Type _} {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
+/- warning: subalgebra.mul_to_submodule_le -> Subalgebra.mul_toSubmodule_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) S T))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (T : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3), LE.le.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Preorder.toLE.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (PartialOrder.toPreorder.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (OmegaCompletePartialOrder.toPartialOrder.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (CompleteLattice.instOmegaCompletePartialOrder.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) T) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A 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(Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) S T))
+Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_leₓ'. -/
 theorem mul_toSubmodule_le (S T : Subalgebra R A) :
     S.toSubmodule * T.toSubmodule ≤ (S ⊔ T).toSubmodule :=
   by
@@ -36,6 +42,12 @@ theorem mul_toSubmodule_le (S T : Subalgebra R A) :
   exact mul_mem (Algebra.mem_sup_left hy) (Algebra.mem_sup_right hz)
 #align subalgebra.mul_to_submodule_le Subalgebra.mul_toSubmodule_le
 
+/- warning: subalgebra.mul_self -> Subalgebra.mul_self is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align subalgebra.mul_self Subalgebra.mul_selfₓ'. -/
 /-- As submodules, subalgebras are idempotent. -/
 @[simp]
 theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubmodule :=
@@ -48,6 +60,12 @@ theorem mul_self (S : Subalgebra R A) : S.toSubmodule * S.toSubmodule = S.toSubm
     exact Submodule.mul_mem_mul hx1 (show (1 : A) ∈ S from one_mem S)
 #align subalgebra.mul_self Subalgebra.mul_self
 
+/- warning: subalgebra.mul_to_submodule -> Subalgebra.mul_toSubmodule is a dubious translation:
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(CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_5)))) (Algebra.toModule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Sup.sup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (SemilatticeSup.toHasSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_4 (CommSemiring.toSemiring.{u2} A _inst_5) _inst_6))))) S T))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : CommSemiring.{u2} R] [_inst_5 : CommSemiring.{u1} A] [_inst_6 : Algebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5)] (S : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (T : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A 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(CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (instHMul.{u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) S) (Submodule.mul.{u2, u1} R _inst_4 A (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} (Subalgebra.{u2, u1} R 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R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) => LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SetLike.instPartialOrder.{u1, u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) => LE.le.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Preorder.toLE.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (PartialOrder.toPreorder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, 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(OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Submodule.completeLattice.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_5)))) (Algebra.toModule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6)) (Sup.sup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (SemilatticeSup.toSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Lattice.toSemilatticeSup.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_4 (CommSemiring.toSemiring.{u1} A _inst_5) _inst_6))))) S T))
+Case conversion may be inaccurate. Consider using '#align subalgebra.mul_to_submodule Subalgebra.mul_toSubmoduleₓ'. -/
 /-- When `A` is commutative, `subalgebra.mul_to_submodule_le` is strict. -/
 theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S T : Subalgebra R A) : S.toSubmodule * T.toSubmodule = (S ⊔ T).toSubmodule :=
@@ -71,6 +89,12 @@ theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring
 
 variable {R' : Type _} [Semiring R'] [MulSemiringAction R' A] [SMulCommClass R' R A]
 
+/- warning: subalgebra.pointwise_mul_action -> Subalgebra.pointwiseMulAction is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))], MulAction.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toSMul.{u3, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)], MulAction.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4))
+Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_mul_action Subalgebra.pointwiseMulActionₓ'. -/
 /-- The action on a subalgebra corresponding to applying the action to every element.
 
 This is available as an instance in the `pointwise` locale. -/
@@ -86,23 +110,47 @@ scoped[Pointwise] attribute [instance] Subalgebra.pointwiseMulAction
 
 open Pointwise
 
+/- warning: subalgebra.coe_pointwise_smul -> Subalgebra.coe_pointwise_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))] (m : R') (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) 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(NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5))))) m ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) S))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u3, u2} R A _inst_1 _inst_2] {R' : Type.{u1}} [_inst_4 : Semiring.{u1} R'] [_inst_5 : MulSemiringAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u1, u3, u2} R' R A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_2 _inst_3)] (m : R') (S : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S)) (HSMul.hSMul.{u1, u2, u2} R' (Set.{u2} A) (Set.{u2} A) (instHSMul.{u1, u2} R' (Set.{u2} A) (Set.smulSet.{u1, u2} R' A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))))) m (SetLike.coe.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_pointwise_smul Subalgebra.coe_pointwise_smulₓ'. -/
 @[simp]
 theorem coe_pointwise_smul (m : R') (S : Subalgebra R A) : ↑(m • S) = m • (S : Set A) :=
   rfl
 #align subalgebra.coe_pointwise_smul Subalgebra.coe_pointwise_smul
 
+/- warning: subalgebra.pointwise_smul_to_subsemiring -> Subalgebra.pointwise_smul_toSubsemiring is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))] (m : R') (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 (SMul.smul.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toHasSmul.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u1, u2, u3} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6)) m S)) (SMul.smul.{u3, u2} R' (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (MulAction.toHasSmul.{u3, u2} R' (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (Subsemiring.pointwiseMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)) m (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3 S))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u3, u2} R A _inst_1 _inst_2] {R' : Type.{u1}} [_inst_4 : Semiring.{u1} R'] [_inst_5 : MulSemiringAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u1, u3, u2} R' R A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_2 _inst_3)] (m : R') (S : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subalgebra.toSubsemiring.{u3, u2} R A _inst_1 _inst_2 _inst_3 (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S)) (HSMul.hSMul.{u1, u2, u2} R' (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (instHSMul.{u1, u2} R' (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (MulAction.toSMul.{u1, u2} R' (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subsemiring.pointwiseMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5))) m (Subalgebra.toSubsemiring.{u3, u2} R A _inst_1 _inst_2 _inst_3 S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_smul_to_subsemiring Subalgebra.pointwise_smul_toSubsemiringₓ'. -/
 @[simp]
 theorem pointwise_smul_toSubsemiring (m : R') (S : Subalgebra R A) :
     (m • S).toSubsemiring = m • S.toSubsemiring :=
   rfl
 #align subalgebra.pointwise_smul_to_subsemiring Subalgebra.pointwise_smul_toSubsemiring
 
+/- warning: subalgebra.pointwise_smul_to_submodule -> Subalgebra.pointwise_smul_toSubmodule is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' 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_inst_3) (MulAction.toHasSmul.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u1, u2, u3} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6)) m S)) (SMul.smul.{u3, u2} R' (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SMulZeroClass.toHasSmul.{u3, u2} R' (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddZeroClass.toHasZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoid.toAddZeroClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoid.toAddZeroClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (DistribMulAction.toDistribSMul.{u3, u2} R' (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.pointwiseDistribMulAction.{u3, u1, u2} R' R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5) _inst_6)))) m (coeFn.{succ u2, succ u2} (OrderEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (fun (_x : RelEmbedding.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) => (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) -> (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (RelEmbedding.hasCoeToFun.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.partialOrder.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))))) (Subalgebra.toSubmodule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u3, u2} R A _inst_1 _inst_2] {R' : Type.{u1}} [_inst_4 : Semiring.{u1} R'] [_inst_5 : MulSemiringAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u1, u3, u2} R' R A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_2 _inst_3)] (m : R') (S : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3), Eq.{succ u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S)) (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (fun (_x : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Function.instEmbeddingLikeEmbedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) (RelEmbedding.toEmbedding.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S)) (HSMul.hSMul.{u1, u2, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (instHSMul.{u1, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (SMulZeroClass.toSMul.{u1, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (MonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toMonoidWithZero.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (IdemSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.idemSemiring.{u3, u2} R _inst_1 A _inst_2 _inst_3)))) (DistribSMul.toSMulZeroClass.{u1, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddMonoidWithOne.toAddMonoid.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (IdemSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (Submodule.idemSemiring.{u3, u2} R _inst_1 A _inst_2 _inst_3))))))) (DistribMulAction.toDistribSMul.{u1, u2} R' ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A 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(Submodule.pointwiseDistribMulAction.{u1, u3, u2} R' R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5) _inst_6))))) m (FunLike.coe.{succ u2, succ u2, succ u2} (Function.Embedding.{succ u2, succ u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3))) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) 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Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) => LE.le.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Preorder.toLE.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (PartialOrder.toPreorder.{u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instPartialOrder.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)))) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) => LE.le.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u3, u2} R A _inst_1 _inst_2 _inst_3)))))) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (Subalgebra.toSubmodule.{u3, u2} R A _inst_1 _inst_2 _inst_3)) S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmoduleₓ'. -/
 @[simp]
 theorem pointwise_smul_toSubmodule (m : R') (S : Subalgebra R A) :
     (m • S).toSubmodule = m • S.toSubmodule :=
   rfl
 #align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmodule
 
+/- warning: subalgebra.pointwise_smul_to_subring -> Subalgebra.pointwise_smul_toSubring is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R' : Type.{u3}} {R : Type.{u2}} {A : Type.{u1}} [_inst_7 : Semiring.{u3} R'] [_inst_8 : CommRing.{u2} R] [_inst_9 : Ring.{u1} A] [_inst_10 : MulSemiringAction.{u3, u1} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_7)) (Ring.toSemiring.{u1} A _inst_9)] [_inst_11 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9)] [_inst_12 : SMulCommClass.{u3, u2, u1} R' R A (SMulZeroClass.toSMul.{u3, u1} R' A (MonoidWithZero.toZero.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A _inst_9))) (DistribSMul.toSMulZeroClass.{u3, u1} R' A (AddMonoid.toAddZeroClass.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddGroupWithOne.toAddMonoidWithOne.{u1} A (Ring.toAddGroupWithOne.{u1} A _inst_9)))) (DistribMulAction.toDistribSMul.{u3, u1} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_7)) (AddMonoidWithOne.toAddMonoid.{u1} A (AddGroupWithOne.toAddMonoidWithOne.{u1} A (Ring.toAddGroupWithOne.{u1} A _inst_9))) (MulSemiringAction.toDistribMulAction.{u3, u1} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_7)) (Ring.toSemiring.{u1} A _inst_9) _inst_10)))) (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_11)] (m : R') (S : Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_11), Eq.{succ u1} (Subring.{u1} A _inst_9) (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_11 (HSMul.hSMul.{u3, u1, u1} R' (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_11) (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_11) (instHSMul.{u3, u1} R' (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_11) (MulAction.toSMul.{u3, u1} R' (Subalgebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_11) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_7)) (Subalgebra.pointwiseMulAction.{u2, u1, u3} R A (CommRing.toCommSemiring.{u2} R _inst_8) (Ring.toSemiring.{u1} A _inst_9) _inst_11 R' _inst_7 _inst_10 _inst_12))) m S)) (HSMul.hSMul.{u3, u1, u1} R' (Subring.{u1} A _inst_9) (Subring.{u1} A _inst_9) (instHSMul.{u3, u1} R' (Subring.{u1} A _inst_9) (MulAction.toSMul.{u3, u1} R' (Subring.{u1} A _inst_9) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_7)) (Subring.pointwiseMulAction.{u3, u1} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_7)) _inst_9 _inst_10))) m (Subalgebra.toSubring.{u2, u1} R A _inst_8 _inst_9 _inst_11 S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.pointwise_smul_to_subring Subalgebra.pointwise_smul_toSubringₓ'. -/
 @[simp]
 theorem pointwise_smul_toSubring {R' R A : Type _} [Semiring R'] [CommRing R] [Ring A]
     [MulSemiringAction R' A] [Algebra R A] [SMulCommClass R' R A] (m : R') (S : Subalgebra R A) :
@@ -110,6 +158,12 @@ theorem pointwise_smul_toSubring {R' R A : Type _} [Semiring R'] [CommRing R] [R
   rfl
 #align subalgebra.pointwise_smul_to_subring Subalgebra.pointwise_smul_toSubring
 
+/- warning: subalgebra.smul_mem_pointwise_smul -> Subalgebra.smul_mem_pointwise_smul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {R' : Type.{u3}} [_inst_4 : Semiring.{u3} R'] [_inst_5 : MulSemiringAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} R' R A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))] (m : R') (r : A) (S : Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3), (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) r S) -> (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SMul.smul.{u3, u2} R' A (SMulZeroClass.toHasSmul.{u3, u2} R' A (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_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} R' A (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) _inst_2 _inst_5)))) m r) (SMul.smul.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toHasSmul.{u3, u2} R' (Subalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u3} R' (Semiring.toMonoidWithZero.{u3} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u1, u2, u3} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6)) m S))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u3, u2} R A _inst_1 _inst_2] {R' : Type.{u1}} [_inst_4 : Semiring.{u1} R'] [_inst_5 : MulSemiringAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2] [_inst_6 : SMulCommClass.{u1, u3, u2} R' R A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5)))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_2 _inst_3)] (m : R') (r : A) (S : Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3), (Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)) r S) -> (Membership.mem.{u2, u2} A (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (SetLike.instMembership.{u2, u2} (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3)) (HSMul.hSMul.{u1, u2, u2} R' A A (instHSMul.{u1, u2} R' A (SMulZeroClass.toSMul.{u1, u2} R' A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R' A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u1, u2} R' A (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) _inst_2 _inst_5))))) m r) (HSMul.hSMul.{u1, u2, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (instHSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MulAction.toSMul.{u1, u2} R' (Subalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3) (MonoidWithZero.toMonoid.{u1} R' (Semiring.toMonoidWithZero.{u1} R' _inst_4)) (Subalgebra.pointwiseMulAction.{u3, u2, u1} R A _inst_1 _inst_2 _inst_3 R' _inst_4 _inst_5 _inst_6))) m S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.smul_mem_pointwise_smul Subalgebra.smul_mem_pointwise_smulₓ'. -/
 theorem smul_mem_pointwise_smul (m : R') (r : A) (S : Subalgebra R A) : r ∈ S → m • r ∈ m • S :=
   (Set.smul_mem_smul_set : _ → _ ∈ m • (S : Set A))
 #align subalgebra.smul_mem_pointwise_smul Subalgebra.smul_mem_pointwise_smul

b2c707cd

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

b2c707cd

doc: fix many more mathlib3 names in doc comments (#11987)

A mix of various changes; generated with a script and manually tweaked.

2098023c

Diff

@@ -69,7 +69,7 @@ variable {R' : Type*} [Semiring R'] [MulSemiringAction R' A] [SMulCommClass R' R
 
 /-- The action on a subalgebra corresponding to applying the action to every element.
 
-This is available as an instance in the `pointwise` locale. -/
+This is available as an instance in the `Pointwise` locale. -/
 protected def pointwiseMulAction : MulAction R' (Subalgebra R A)
     where
   smul a S := S.map (MulSemiringAction.toAlgHom _ _ a)

b2c707cd

feat: pointwise scalar multiplication is monotone (#11809)

Everywhere we have a smul_mem_pointwise_smul lemma, I've added this result.

5f4e6d8b

Diff

@@ -110,6 +110,9 @@ theorem smul_mem_pointwise_smul (m : R') (r : A) (S : Subalgebra R A) : r ∈ S
   (Set.smul_mem_smul_set : _ → _ ∈ m • (S : Set A))
 #align subalgebra.smul_mem_pointwise_smul Subalgebra.smul_mem_pointwise_smul
 
+instance : CovariantClass R' (Subalgebra R A) HSMul.hSMul LE.le :=
+  ⟨fun _ _ => map_mono⟩
+
 end Pointwise
 
 end Subalgebra

b2c707cd

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

@@ -22,7 +22,7 @@ namespace Subalgebra
 
 section Pointwise
 
-variable {R : Type _} {A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
+variable {R : Type*} {A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
 
 theorem mul_toSubmodule_le (S T : Subalgebra R A) :
     (Subalgebra.toSubmodule S)* (Subalgebra.toSubmodule T) ≤ Subalgebra.toSubmodule (S ⊔ T) := by
@@ -45,7 +45,7 @@ theorem mul_self (S : Subalgebra R A) : (Subalgebra.toSubmodule S) * (Subalgebra
 #align subalgebra.mul_self Subalgebra.mul_self
 
 /-- When `A` is commutative, `Subalgebra.mul_toSubmodule_le` is strict. -/
-theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring A] [Algebra R A]
+theorem mul_toSubmodule {R : Type*} {A : Type*} [CommSemiring R] [CommSemiring A] [Algebra R A]
     (S T : Subalgebra R A) : (Subalgebra.toSubmodule S) * (Subalgebra.toSubmodule T)
         = Subalgebra.toSubmodule (S ⊔ T) := by
   refine' le_antisymm (mul_toSubmodule_le _ _) _
@@ -65,7 +65,7 @@ theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring
     mul_self, mul_comm (Subalgebra.toSubmodule T), ← mul_assoc, mul_self] at this
 #align subalgebra.mul_to_submodule Subalgebra.mul_toSubmodule
 
-variable {R' : Type _} [Semiring R'] [MulSemiringAction R' A] [SMulCommClass R' R A]
+variable {R' : Type*} [Semiring R'] [MulSemiringAction R' A] [SMulCommClass R' R A]
 
 /-- The action on a subalgebra corresponding to applying the action to every element.
 
@@ -100,7 +100,7 @@ theorem pointwise_smul_toSubmodule (m : R') (S : Subalgebra R A) :
 #align subalgebra.pointwise_smul_to_submodule Subalgebra.pointwise_smul_toSubmodule
 
 @[simp]
-theorem pointwise_smul_toSubring {R' R A : Type _} [Semiring R'] [CommRing R] [Ring A]
+theorem pointwise_smul_toSubring {R' R A : Type*} [Semiring R'] [CommRing R] [Ring A]
     [MulSemiringAction R' A] [Algebra R A] [SMulCommClass R' R A] (m : R') (S : Subalgebra R A) :
     (m • S).toSubring = m • S.toSubring :=
   rfl

b2c707cd

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 Weiser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.algebra.subalgebra.pointwise
-! leanprover-community/mathlib commit b2c707cd190a58ea0565c86695a19e99ccecc215
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Operations
 import Mathlib.Algebra.Algebra.Subalgebra.Basic
 import Mathlib.RingTheory.Subring.Pointwise
 import Mathlib.RingTheory.Adjoin.Basic
 
+#align_import algebra.algebra.subalgebra.pointwise from "leanprover-community/mathlib"@"b2c707cd190a58ea0565c86695a19e99ccecc215"
+
 /-!
 # Pointwise actions on subalgebras.

b2c707cd

feat: algebraMap_mem for SetLike instances (#5594)

This adds an algebraMap_mem in the root namespace and protects Subalgebra.algebraMap_mem. The new declaration holds for terms of S where S is a Setlike satisfying OneMemClass S A and SMulMemClass S R A and A is an R-algebra.

6f81a92b

Diff

@@ -62,7 +62,7 @@ theorem mul_toSubmodule {R : Type _} {A : Type _} [CommSemiring R] [CommSemiring
     · rw [← one_mul x]
       exact Submodule.mul_mem_mul (show (1 : A) ∈ S from one_mem S) hxT
   · rw [← one_mul (algebraMap _ _ _)]
-    exact Submodule.mul_mem_mul (show (1 : A) ∈ S from one_mem S) (algebraMap_mem _ _)
+    exact Submodule.mul_mem_mul (show (1 : A) ∈ S from one_mem S) (algebraMap_mem T _)
   have := Submodule.mul_mem_mul hx hy
   rwa [mul_assoc, mul_comm _ (Subalgebra.toSubmodule T), ← mul_assoc _ _ (Subalgebra.toSubmodule S),
     mul_self, mul_comm (Subalgebra.toSubmodule T), ← mul_assoc, mul_self] at this

b2c707cd

feat: port Algebra.Algebra.Subalgebra.Pointwise (#2913)

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

7fb7eebe

`algebra.algebra.subalgebra.pointwise` ⟷ `Mathlib.Algebra.Algebra.Subalgebra.Pointwise`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 458

algebra.algebra.subalgebra.pointwise ⟷ Mathlib.Algebra.Algebra.Subalgebra.Pointwise

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 458

`algebra.algebra.subalgebra.pointwise` ⟷ `Mathlib.Algebra.Algebra.Subalgebra.Pointwise`