topology.algebra.star_subalgebra | 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

b7f5a77f

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

19cb3751

bump to nightly-2024-03-21-08

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

b0154c5c

Diff

@@ -59,7 +59,7 @@ theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
     (hS₁ : IsClosed (S₁ : Set A)) : ClosedEmbedding (inclusion h) :=
   { embedding_inclusion h with
-    closed_range :=
+    isClosed_range :=
       isClosed_induced_iff.2
         ⟨S₁, hS₁, by convert (Set.range_subtype_map id _).symm; rw [Set.image_id]; rfl⟩ }
 #align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusion
@@ -247,7 +247,7 @@ theorem le_of_isClosed_of_mem {S : StarSubalgebra R A} (hS : IsClosed (S : Set A
 theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebra R x → A) :=
   { induced := rfl
     inj := Subtype.coe_injective
-    closed_range := by
+    isClosed_range := by
       convert elementalStarAlgebra.isClosed R x
       exact Set.ext fun y => ⟨by rintro ⟨y, rfl⟩; exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩ }
 #align elemental_star_algebra.closed_embedding_coe elementalStarAlgebra.closedEmbedding_coe

19cb3751

bump to nightly-2024-01-19-06

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

33b57512

Diff

@@ -149,7 +149,7 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
     (h :
       φ.comp (inclusion (le_topologicalClosure S)) = ψ.comp (inclusion (le_topologicalClosure S))) :
     φ = ψ := by
-  rw [FunLike.ext'_iff]
+  rw [DFunLike.ext'_iff]
   have : Dense (Set.range <| inclusion (le_topological_closure S)) :=
     by
     refine' embedding_subtype_coe.to_inducing.dense_iff.2 fun x => _
@@ -158,7 +158,7 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
     exact Set.ext fun y => ⟨by rintro ⟨y, rfl⟩; exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩
   refine' Continuous.ext_on this hφ hψ _
   rintro _ ⟨x, rfl⟩
-  simpa only using FunLike.congr_fun h x
+  simpa only using DFunLike.congr_fun h x
 #align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosure
 -/
 
@@ -173,7 +173,7 @@ theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : Sta
   have : (φ : S.topological_closure →⋆ₐ[R] B) = (ψ : S.topological_closure →⋆ₐ[R] B) := by
     refine' StarAlgHom.ext_topologicalClosure hφ hψ (StarAlgHom.ext _) <;>
       simpa only [StarAlgHom.coe_comp, StarAlgHom.coe_coe] using h
-  simpa only [FunLike.ext'_iff, StarAlgHom.coe_coe]
+  simpa only [DFunLike.ext'_iff, StarAlgHom.coe_coe]
 #align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosure
 -/

19cb3751

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 -/
-import Mathbin.Algebra.Star.Subalgebra
-import Mathbin.Topology.Algebra.Algebra
-import Mathbin.Topology.Algebra.Star
+import Algebra.Star.Subalgebra
+import Topology.Algebra.Algebra
+import Topology.Algebra.Star
 
 #align_import topology.algebra.star_subalgebra from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"

19cb3751

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module topology.algebra.star_subalgebra
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Star.Subalgebra
 import Mathbin.Topology.Algebra.Algebra
 import Mathbin.Topology.Algebra.Star
 
+#align_import topology.algebra.star_subalgebra from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
+
 /-!
 # Topological star (sub)algebras

19cb3751

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -49,12 +49,15 @@ instance [TopologicalSpace R] [ContinuousSMul R A] (s : StarSubalgebra R A) : Co
 instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring s :=
   s.toSubalgebra.TopologicalSemiring
 
+#print StarSubalgebra.embedding_inclusion /-
 /-- The `star_subalgebra.inclusion` of a star subalgebra is an `embedding`. -/
 theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : Embedding (inclusion h) :=
   { induced := Eq.symm induced_compose
     inj := Subtype.map_injective h Function.injective_id }
 #align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusion
+-/
 
+#print StarSubalgebra.closedEmbedding_inclusion /-
 /-- The `star_subalgebra.inclusion` of a closed star subalgebra is a `closed_embedding`. -/
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
     (hS₁ : IsClosed (S₁ : Set A)) : ClosedEmbedding (inclusion h) :=
@@ -63,6 +66,7 @@ theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤
       isClosed_induced_iff.2
         ⟨S₁, hS₁, by convert (Set.range_subtype_map id _).symm; rw [Set.image_id]; rfl⟩ }
 #align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusion
+-/
 
 variable [TopologicalSemiring A] [ContinuousStar A]
 
@@ -79,30 +83,38 @@ def topologicalClosure (s : StarSubalgebra R A) : StarSubalgebra R A :=
 #align star_subalgebra.topological_closure StarSubalgebra.topologicalClosure
 -/
 
+#print StarSubalgebra.topologicalClosure_coe /-
 @[simp]
 theorem topologicalClosure_coe (s : StarSubalgebra R A) :
     (s.topologicalClosure : Set A) = closure (s : Set A) :=
   rfl
 #align star_subalgebra.topological_closure_coe StarSubalgebra.topologicalClosure_coe
+-/
 
+#print StarSubalgebra.le_topologicalClosure /-
 theorem le_topologicalClosure (s : StarSubalgebra R A) : s ≤ s.topologicalClosure :=
   subset_closure
 #align star_subalgebra.le_topological_closure StarSubalgebra.le_topologicalClosure
+-/
 
+#print StarSubalgebra.isClosed_topologicalClosure /-
 theorem isClosed_topologicalClosure (s : StarSubalgebra R A) :
     IsClosed (s.topologicalClosure : Set A) :=
   isClosed_closure
 #align star_subalgebra.is_closed_topological_closure StarSubalgebra.isClosed_topologicalClosure
+-/
 
 instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing A]
     [TopologicalSemiring A] [ContinuousStar A] [Algebra R A] [StarModule R A]
     {S : StarSubalgebra R A} : CompleteSpace S.topologicalClosure :=
   isClosed_closure.completeSpace_coe
 
+#print StarSubalgebra.topologicalClosure_minimal /-
 theorem topologicalClosure_minimal {s t : StarSubalgebra R A} (h : s ≤ t)
     (ht : IsClosed (t : Set A)) : s.topologicalClosure ≤ t :=
   closure_minimal h ht
 #align star_subalgebra.topological_closure_minimal StarSubalgebra.topologicalClosure_minimal
+-/
 
 #print StarSubalgebra.topologicalClosure_mono /-
 theorem topologicalClosure_mono : Monotone (topologicalClosure : _ → StarSubalgebra R A) :=
@@ -111,6 +123,7 @@ theorem topologicalClosure_mono : Monotone (topologicalClosure : _ → StarSubal
 #align star_subalgebra.topological_closure_mono StarSubalgebra.topologicalClosure_mono
 -/
 
+#print StarSubalgebra.commSemiringTopologicalClosure /-
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
 @[reducible]
@@ -118,7 +131,9 @@ def commSemiringTopologicalClosure [T2Space A] (s : StarSubalgebra R A)
     (hs : ∀ x y : s, x * y = y * x) : CommSemiring s.topologicalClosure :=
   s.toSubalgebra.commSemiringTopologicalClosure hs
 #align star_subalgebra.comm_semiring_topological_closure StarSubalgebra.commSemiringTopologicalClosure
+-/
 
+#print StarSubalgebra.commRingTopologicalClosure /-
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
 @[reducible]
@@ -127,7 +142,9 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
     (s : StarSubalgebra R A) (hs : ∀ x y : s, x * y = y * x) : CommRing s.topologicalClosure :=
   s.toSubalgebra.commRingTopologicalClosure hs
 #align star_subalgebra.comm_ring_topological_closure StarSubalgebra.commRingTopologicalClosure
+-/
 
+#print StarAlgHom.ext_topologicalClosure /-
 /-- Continuous `star_alg_hom`s from the the topological closure of a `star_subalgebra` whose
 compositions with the `star_subalgebra.inclusion` map agree are, in fact, equal. -/
 theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
@@ -146,7 +163,9 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
   rintro _ ⟨x, rfl⟩
   simpa only using FunLike.congr_fun h x
 #align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosure
+-/
 
+#print StarAlgHomClass.ext_topologicalClosure /-
 theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : StarSubalgebra R A}
     [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F} (hφ : Continuous φ) (hψ : Continuous ψ)
     (h :
@@ -159,6 +178,7 @@ theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : Sta
       simpa only [StarAlgHom.coe_comp, StarAlgHom.coe_coe] using h
   simpa only [FunLike.ext'_iff, StarAlgHom.coe_coe]
 #align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosure
+-/
 
 end TopologicalStarAlgebra
 
@@ -218,10 +238,12 @@ instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing
     CompleteSpace (elementalStarAlgebra R x) :=
   isClosed_closure.completeSpace_coe
 
+#print elementalStarAlgebra.le_of_isClosed_of_mem /-
 theorem le_of_isClosed_of_mem {S : StarSubalgebra R A} (hS : IsClosed (S : Set A)) {x : A}
     (hx : x ∈ S) : elementalStarAlgebra R x ≤ S :=
   topologicalClosure_minimal (adjoin_le <| Set.singleton_subset_iff.2 hx) hS
 #align elemental_star_algebra.le_of_is_closed_of_mem elementalStarAlgebra.le_of_isClosed_of_mem
+-/
 
 #print elementalStarAlgebra.closedEmbedding_coe /-
 /-- The coercion from an elemental algebra to the full algebra as a `closed_embedding`. -/
@@ -234,6 +256,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
 #align elemental_star_algebra.closed_embedding_coe elementalStarAlgebra.closedEmbedding_coe
 -/
 
+#print elementalStarAlgebra.starAlgHomClass_ext /-
 theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)
     (hψ : Continuous ψ) (h : φ ⟨a, self_mem R a⟩ = ψ ⟨a, self_mem R a⟩) : φ = ψ :=
@@ -243,6 +266,7 @@ theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     simp only [AlgHomClass.commutes], fun x y hx hy => by simp only [map_add, hx, hy],
     fun x y hx hy => by simp only [map_mul, hx, hy], fun x hx => by simp only [map_star, hx]]
 #align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_ext
+-/
 
 end elementalStarAlgebra

19cb3751

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -61,7 +61,7 @@ theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤
   { embedding_inclusion h with
     closed_range :=
       isClosed_induced_iff.2
-        ⟨S₁, hS₁, by convert(Set.range_subtype_map id _).symm; rw [Set.image_id]; rfl⟩ }
+        ⟨S₁, hS₁, by convert (Set.range_subtype_map id _).symm; rw [Set.image_id]; rfl⟩ }
 #align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusion
 
 variable [TopologicalSemiring A] [ContinuousStar A]

19cb3751

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -239,7 +239,7 @@ theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     (hψ : Continuous ψ) (h : φ ⟨a, self_mem R a⟩ = ψ ⟨a, self_mem R a⟩) : φ = ψ :=
   by
   refine' StarAlgHomClass.ext_topologicalClosure hφ hψ fun x => adjoin_induction' x _ _ _ _ _
-  exacts[fun y hy => by simpa only [set.mem_singleton_iff.mp hy] using h, fun r => by
+  exacts [fun y hy => by simpa only [set.mem_singleton_iff.mp hy] using h, fun r => by
     simp only [AlgHomClass.commutes], fun x y hx hy => by simp only [map_add, hx, hy],
     fun x y hx hy => by simp only [map_mul, hx, hy], fun x hx => by simp only [map_star, hx]]
 #align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_ext

19cb3751

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -33,7 +33,7 @@ which as a star algebra is a topological star algebra.
 
 open Classical Set TopologicalSpace
 
-open Classical
+open scoped Classical
 
 namespace StarSubalgebra

19cb3751

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -49,18 +49,12 @@ instance [TopologicalSpace R] [ContinuousSMul R A] (s : StarSubalgebra R A) : Co
 instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring s :=
   s.toSubalgebra.TopologicalSemiring
 
-/- warning: star_subalgebra.embedding_inclusion -> StarSubalgebra.embedding_inclusion is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a star subalgebra is an `embedding`. -/
 theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : Embedding (inclusion h) :=
   { induced := Eq.symm induced_compose
     inj := Subtype.map_injective h Function.injective_id }
 #align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusion
 
-/- warning: star_subalgebra.closed_embedding_inclusion -> StarSubalgebra.closedEmbedding_inclusion is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a closed star subalgebra is a `closed_embedding`. -/
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
     (hS₁ : IsClosed (S₁ : Set A)) : ClosedEmbedding (inclusion h) :=
@@ -85,34 +79,16 @@ def topologicalClosure (s : StarSubalgebra R A) : StarSubalgebra R A :=
 #align star_subalgebra.topological_closure StarSubalgebra.topologicalClosure
 -/
 
-/- warning: star_subalgebra.topological_closure_coe -> StarSubalgebra.topologicalClosure_coe is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s)) (closure.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) s))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.topological_closure_coe StarSubalgebra.topologicalClosure_coeₓ'. -/
 @[simp]
 theorem topologicalClosure_coe (s : StarSubalgebra R A) :
     (s.topologicalClosure : Set A) = closure (s : Set A) :=
   rfl
 #align star_subalgebra.topological_closure_coe StarSubalgebra.topologicalClosure_coe
 
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.le_topological_closure StarSubalgebra.le_topologicalClosureₓ'. -/
 theorem le_topologicalClosure (s : StarSubalgebra R A) : s ≤ s.topologicalClosure :=
   subset_closure
 #align star_subalgebra.le_topological_closure StarSubalgebra.le_topologicalClosure
 
-/- warning: star_subalgebra.is_closed_topological_closure -> StarSubalgebra.isClosed_topologicalClosure is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s))
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s))
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.is_closed_topological_closure StarSubalgebra.isClosed_topologicalClosureₓ'. -/
 theorem isClosed_topologicalClosure (s : StarSubalgebra R A) :
     IsClosed (s.topologicalClosure : Set A) :=
   isClosed_closure
@@ -123,9 +99,6 @@ instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing
     {S : StarSubalgebra R A} : CompleteSpace S.topologicalClosure :=
   isClosed_closure.completeSpace_coe
 
-/- warning: star_subalgebra.topological_closure_minimal -> StarSubalgebra.topologicalClosure_minimal is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.topological_closure_minimal StarSubalgebra.topologicalClosure_minimalₓ'. -/
 theorem topologicalClosure_minimal {s t : StarSubalgebra R A} (h : s ≤ t)
     (ht : IsClosed (t : Set A)) : s.topologicalClosure ≤ t :=
   closure_minimal h ht
@@ -138,9 +111,6 @@ theorem topologicalClosure_mono : Monotone (topologicalClosure : _ → StarSubal
 #align star_subalgebra.topological_closure_mono StarSubalgebra.topologicalClosure_mono
 -/
 
-/- warning: star_subalgebra.comm_semiring_topological_closure -> StarSubalgebra.commSemiringTopologicalClosure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.comm_semiring_topological_closure StarSubalgebra.commSemiringTopologicalClosureₓ'. -/
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
 @[reducible]
@@ -149,9 +119,6 @@ def commSemiringTopologicalClosure [T2Space A] (s : StarSubalgebra R A)
   s.toSubalgebra.commSemiringTopologicalClosure hs
 #align star_subalgebra.comm_semiring_topological_closure StarSubalgebra.commSemiringTopologicalClosure
 
-/- warning: star_subalgebra.comm_ring_topological_closure -> StarSubalgebra.commRingTopologicalClosure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.comm_ring_topological_closure StarSubalgebra.commRingTopologicalClosureₓ'. -/
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
 @[reducible]
@@ -161,9 +128,6 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
   s.toSubalgebra.commRingTopologicalClosure hs
 #align star_subalgebra.comm_ring_topological_closure StarSubalgebra.commRingTopologicalClosure
 
-/- warning: star_alg_hom.ext_topological_closure -> StarAlgHom.ext_topologicalClosure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosureₓ'. -/
 /-- Continuous `star_alg_hom`s from the the topological closure of a `star_subalgebra` whose
 compositions with the `star_subalgebra.inclusion` map agree are, in fact, equal. -/
 theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
@@ -183,9 +147,6 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
   simpa only using FunLike.congr_fun h x
 #align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosure
 
-/- warning: star_alg_hom_class.ext_topological_closure -> StarAlgHomClass.ext_topologicalClosure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosureₓ'. -/
 theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : StarSubalgebra R A}
     [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F} (hφ : Continuous φ) (hψ : Continuous ψ)
     (h :
@@ -257,9 +218,6 @@ instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing
     CompleteSpace (elementalStarAlgebra R x) :=
   isClosed_closure.completeSpace_coe
 
-/- warning: elemental_star_algebra.le_of_is_closed_of_mem -> elementalStarAlgebra.le_of_isClosed_of_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.le_of_is_closed_of_mem elementalStarAlgebra.le_of_isClosed_of_memₓ'. -/
 theorem le_of_isClosed_of_mem {S : StarSubalgebra R A} (hS : IsClosed (S : Set A)) {x : A}
     (hx : x ∈ S) : elementalStarAlgebra R x ≤ S :=
   topologicalClosure_minimal (adjoin_le <| Set.singleton_subset_iff.2 hx) hS
@@ -276,9 +234,6 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
 #align elemental_star_algebra.closed_embedding_coe elementalStarAlgebra.closedEmbedding_coe
 -/
 
-/- warning: elemental_star_algebra.star_alg_hom_class_ext -> elementalStarAlgebra.starAlgHomClass_ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_extₓ'. -/
 theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)
     (hψ : Continuous ψ) (h : φ ⟨a, self_mem R a⟩ = ψ ⟨a, self_mem R a⟩) : φ = ψ :=

19cb3751

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -67,10 +67,7 @@ theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤
   { embedding_inclusion h with
     closed_range :=
       isClosed_induced_iff.2
-        ⟨S₁, hS₁, by
-          convert(Set.range_subtype_map id _).symm
-          rw [Set.image_id]
-          rfl⟩ }
+        ⟨S₁, hS₁, by convert(Set.range_subtype_map id _).symm; rw [Set.image_id]; rfl⟩ }
 #align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusion
 
 variable [TopologicalSemiring A] [ContinuousStar A]
@@ -180,11 +177,7 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
     refine' embedding_subtype_coe.to_inducing.dense_iff.2 fun x => _
     convert show ↑x ∈ closure (S : Set A) from x.prop
     rw [← Set.range_comp]
-    exact
-      Set.ext fun y =>
-        ⟨by
-          rintro ⟨y, rfl⟩
-          exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩
+    exact Set.ext fun y => ⟨by rintro ⟨y, rfl⟩; exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩
   refine' Continuous.ext_on this hφ hψ _
   rintro _ ⟨x, rfl⟩
   simpa only using FunLike.congr_fun h x
@@ -279,11 +272,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
     inj := Subtype.coe_injective
     closed_range := by
       convert elementalStarAlgebra.isClosed R x
-      exact
-        Set.ext fun y =>
-          ⟨by
-            rintro ⟨y, rfl⟩
-            exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩ }
+      exact Set.ext fun y => ⟨by rintro ⟨y, rfl⟩; exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩ }
 #align elemental_star_algebra.closed_embedding_coe elementalStarAlgebra.closedEmbedding_coe
 -/

19cb3751

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -50,10 +50,7 @@ instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring
   s.toSubalgebra.TopologicalSemiring
 
 /- warning: star_subalgebra.embedding_inclusion -> StarSubalgebra.embedding_inclusion is a dubious translation:
-lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toHasLe.{u2} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a star subalgebra is an `embedding`. -/
 theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : Embedding (inclusion h) :=
@@ -62,10 +59,7 @@ theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 #align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusion
 
 /- warning: star_subalgebra.closed_embedding_inclusion -> StarSubalgebra.closedEmbedding_inclusion is a dubious translation:
-lean 3 declaration is
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(AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) S₁)) -> (ClosedEmbedding.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₂) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁) _inst_3) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂) _inst_3) (coeFn.{succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ 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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a closed star subalgebra is a `closed_embedding`. -/
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
@@ -133,10 +127,7 @@ instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing
   isClosed_closure.completeSpace_coe
 
 /- warning: star_subalgebra.topological_closure_minimal -> StarSubalgebra.topologicalClosure_minimal is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.topological_closure_minimal StarSubalgebra.topologicalClosure_minimalₓ'. -/
 theorem topologicalClosure_minimal {s t : StarSubalgebra R A} (h : s ≤ t)
     (ht : IsClosed (t : Set A)) : s.topologicalClosure ≤ t :=
@@ -151,10 +142,7 @@ theorem topologicalClosure_mono : Monotone (topologicalClosure : _ → StarSubal
 -/
 
 /- warning: star_subalgebra.comm_semiring_topological_closure -> StarSubalgebra.commSemiringTopologicalClosure is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comm_semiring_topological_closure StarSubalgebra.commSemiringTopologicalClosureₓ'. -/
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
@@ -165,10 +153,7 @@ def commSemiringTopologicalClosure [T2Space A] (s : StarSubalgebra R A)
 #align star_subalgebra.comm_semiring_topological_closure StarSubalgebra.commSemiringTopologicalClosure
 
 /- warning: star_subalgebra.comm_ring_topological_closure -> StarSubalgebra.commRingTopologicalClosure is a dubious translation:
-lean 3 declaration is
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(NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14))) _inst_15))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17)) _inst_19))) (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 (Ring.toSemiring.{u2} A _inst_17))))))) (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 (CommRing.toCommSemiring.{u1} R _inst_14)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_14))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_14)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17) _inst_18)))))] [_inst_21 : TopologicalRing.{u2} A _inst_16 (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_17))] [_inst_22 : ContinuousStar.{u2} A _inst_16 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17)) _inst_19)))] [_inst_23 : T2Space.{u2} A _inst_16] (s : StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20), (forall (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) s) (y : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R 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-but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_14 : CommRing.{u1} R] [_inst_15 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14)))] [_inst_16 : TopologicalSpace.{u2} A] [_inst_17 : Ring.{u2} A] [_inst_18 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17)] [_inst_19 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17))] [_inst_20 : StarModule.{u1, u2} R A (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_14)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14))) _inst_15))) (InvolutiveStar.toStar.{u2} A 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_inst_19 _inst_20 (TopologicalRing.toTopologicalSemiring.{u2} A _inst_16 (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_17)) _inst_21) _inst_22 s))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comm_ring_topological_closure StarSubalgebra.commRingTopologicalClosureₓ'. -/
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
@@ -180,10 +165,7 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
 #align star_subalgebra.comm_ring_topological_closure StarSubalgebra.commRingTopologicalClosure
 
 /- warning: star_alg_hom.ext_topological_closure -> StarAlgHom.ext_topologicalClosure is a dubious translation:
-lean 3 declaration is
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(AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosureₓ'. -/
 /-- Continuous `star_alg_hom`s from the the topological closure of a `star_subalgebra` whose
 compositions with the `star_subalgebra.inclusion` map agree are, in fact, equal. -/
@@ -209,10 +191,7 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
 #align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosure
 
 /- warning: star_alg_hom_class.ext_topological_closure -> StarAlgHomClass.ext_topologicalClosure is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A 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(StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u3} F φ ψ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosureₓ'. -/
 theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : StarSubalgebra R A}
     [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F} (hφ : Continuous φ) (hψ : Continuous ψ)
@@ -286,10 +265,7 @@ instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing
   isClosed_closure.completeSpace_coe
 
 /- warning: elemental_star_algebra.le_of_is_closed_of_mem -> elementalStarAlgebra.le_of_isClosed_of_mem is a dubious translation:
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R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9}, (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)))) S)) -> (forall {x : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x S) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_8 _inst_5 _inst_9))))) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 x) S))
-but is expected to have type
-  forall (R : Type.{u2}) {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9}, (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) S)) -> (forall {x : A}, (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x S) -> (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (OmegaCompletePartialOrder.toPartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_8 _inst_5 _inst_9))))) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 x) S))
+<too large>
 Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.le_of_is_closed_of_mem elementalStarAlgebra.le_of_isClosed_of_memₓ'. -/
 theorem le_of_isClosed_of_mem {S : StarSubalgebra R A} (hS : IsClosed (S : Set A)) {x : A}
     (hx : x ∈ S) : elementalStarAlgebra R x ≤ S :=
@@ -312,10 +288,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
 -/
 
 /- warning: elemental_star_algebra.star_alg_hom_class_ext -> elementalStarAlgebra.starAlgHomClass_ext is a dubious translation:
-lean 3 declaration is
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_inst_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8)))))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_13 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {a : A} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 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(StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) φ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 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(StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_extₓ'. -/
 theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)

19cb3751

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -53,7 +53,7 @@ instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toHasLe.{u2} 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 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), Embedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 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A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a star subalgebra is an `embedding`. -/
 theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : Embedding (inclusion h) :=
@@ -65,7 +65,7 @@ theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) S₁)) -> (ClosedEmbedding.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₂) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁) _inst_3) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂) _inst_3) (coeFn.{succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ 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 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁)) -> (ClosedEmbedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A 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 Case conversion may be inaccurate. Consider using '#align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a closed star subalgebra is a `closed_embedding`. -/
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
@@ -183,7 +183,7 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))} {ψ : StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 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(Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))}, (Continuous.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 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_inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B 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_inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 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_inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))}, (Continuous.{u1, u3} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) φ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarAlgHom.comp.{u2, u1, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) 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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u1) (succ u3)} (StarAlgHom.{u2, u1, u3} R 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(StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))} {ψ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 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(StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) φ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarAlgHom.comp.{u2, u1, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u1) (succ u3)} (StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosureₓ'. -/
 /-- Continuous `star_alg_hom`s from the the topological closure of a `star_subalgebra` whose
 compositions with the `star_subalgebra.inclusion` map agree are, in fact, equal. -/
@@ -212,7 +212,7 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u4} F φ ψ)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13)))] {φ : F} {ψ : F}, (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13))) _inst_15)) φ)) -> (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x 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_inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u3} F φ ψ)
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 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(StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u3} F φ ψ)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosureₓ'. -/
 theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : StarSubalgebra R A}
     [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F} (hφ : Continuous φ) (hψ : Continuous ψ)
@@ -315,7 +315,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_6 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_7 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8)))))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_13 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {a : A} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A 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 but is expected to have type
-  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} 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[_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {a : A} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 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(Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) φ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, 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(SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
+  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_13 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {a : A} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12)))] {φ : F} {ψ : F}, (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x 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 Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_extₓ'. -/
 theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)

19cb3751

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -51,7 +51,7 @@ instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring
 
 /- warning: star_subalgebra.embedding_inclusion -> StarSubalgebra.embedding_inclusion is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A 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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A 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 but is expected to have type
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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A 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(StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHomClass.toStarHomClass.{u1, u2, u1, u1} (StarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 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(StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusionₓ'. -/
@@ -63,7 +63,7 @@ theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 
 /- warning: star_subalgebra.closed_embedding_inclusion -> StarSubalgebra.closedEmbedding_inclusion is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A _inst_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} 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+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toHasLe.{u2} 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusionₓ'. -/
@@ -108,7 +108,7 @@ theorem topologicalClosure_coe (s : StarSubalgebra R A) :
 
 /- warning: star_subalgebra.le_topological_closure -> StarSubalgebra.le_topologicalClosure is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s)
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.le_topological_closure StarSubalgebra.le_topologicalClosureₓ'. -/
@@ -134,7 +134,7 @@ instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing
 
 /- warning: star_subalgebra.topological_closure_minimal -> StarSubalgebra.topologicalClosure_minimal is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] {s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {t : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s t) -> (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) t)) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s) t)
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] {s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {t : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s t) -> (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) t)) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s) t)
 but is expected to have type
   forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] {s : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {t : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7}, (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s t) -> (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) t)) -> (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s) t)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.topological_closure_minimal StarSubalgebra.topologicalClosure_minimalₓ'. -/
@@ -287,7 +287,7 @@ instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing
 
 /- warning: elemental_star_algebra.le_of_is_closed_of_mem -> elementalStarAlgebra.le_of_isClosed_of_mem is a dubious translation:
 lean 3 declaration is
-  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_6 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_7 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9}, (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)))) S)) -> (forall {x : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x S) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_8 _inst_5 _inst_9))))) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 x) S))
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_6 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_7 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9}, (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)))) S)) -> (forall {x : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x S) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_8 _inst_5 _inst_9))))) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 x) S))
 but is expected to have type
   forall (R : Type.{u2}) {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9}, (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) S)) -> (forall {x : A}, (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x S) -> (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (OmegaCompletePartialOrder.toPartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_8 _inst_5 _inst_9))))) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 x) S))
 Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.le_of_is_closed_of_mem elementalStarAlgebra.le_of_isClosed_of_memₓ'. -/

19cb3751

bump to nightly-2023-05-16-14

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

b356e20f

Diff

@@ -53,7 +53,7 @@ instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), Embedding.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₂) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁) _inst_3) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂) _inst_3) (coeFn.{succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁ A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂ A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) 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 but is expected to have type
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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 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_inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A 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+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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(StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a star subalgebra is an `embedding`. -/
 theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : Embedding (inclusion h) :=
@@ -65,7 +65,7 @@ theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) S₁)) -> (ClosedEmbedding.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₂) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁) _inst_3) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂) _inst_3) (coeFn.{succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ 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_inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h)))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁)) -> (ClosedEmbedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A 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_inst_6 _inst_5 _inst_7)) x S₁)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _x) (StarHomClass.toFunLike.{u1, u1, u1} (StarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_6 _inst_5 _inst_7)) x S₁)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _x) (StarHomClass.toFunLike.{u1, u1, u1} (StarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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(AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHomClass.toStarHomClass.{u1, u2, u1, u1} (StarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 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_inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a closed star subalgebra is a `closed_embedding`. -/
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
@@ -183,7 +183,7 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 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(AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B 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_inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))}, (Continuous.{u1, u3} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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_inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (fun (_x : Subtype.{succ u1} 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(StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u1) (succ u3)} (StarAlgHom.{u2, u1, u3} R 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(StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))} {ψ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 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(InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))}, (Continuous.{u1, u3} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) φ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarAlgHom.comp.{u2, u1, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u1) (succ u3)} (StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosureₓ'. -/
 /-- Continuous `star_alg_hom`s from the the topological closure of a `star_subalgebra` whose
 compositions with the `star_subalgebra.inclusion` map agree are, in fact, equal. -/
@@ -212,7 +212,7 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A 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 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13)))] {φ : F} {ψ : F}, (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13))) _inst_15)) φ)) -> (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) 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(StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A 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_inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u3} F φ ψ)
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B 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_inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u3} F φ ψ)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosureₓ'. -/
 theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : StarSubalgebra R A}
     [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F} (hφ : Continuous φ) (hψ : Continuous ψ)
@@ -315,7 +315,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_6 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_7 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8)))))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_13 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {a : A} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A 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 but is expected to have type
-  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} 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(elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 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(SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
+  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_13 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {a : A} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B 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(elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 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_inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
 Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_extₓ'. -/
 theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)

19cb3751

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -53,7 +53,7 @@ instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), Embedding.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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(StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
 but is expected to have type
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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), Embedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), Embedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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(Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHomClass.toStarHomClass.{u1, u2, u1, u1} (StarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) 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A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a star subalgebra is an `embedding`. -/
 theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : Embedding (inclusion h) :=
@@ -65,7 +65,7 @@ theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) 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(StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂ A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h)))
 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁)) -> (ClosedEmbedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A 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(StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHomClass.toStarHomClass.{u1, u2, u1, u1} (StarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a closed star subalgebra is a `closed_embedding`. -/
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
@@ -168,7 +168,7 @@ def commSemiringTopologicalClosure [T2Space A] (s : StarSubalgebra R A)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_14 : CommRing.{u1} R] [_inst_15 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14)))] [_inst_16 : TopologicalSpace.{u2} A] [_inst_17 : Ring.{u2} A] [_inst_18 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17)] [_inst_19 : StarRing.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17))] [_inst_20 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14))) _inst_15))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17)) _inst_19))) (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 (Ring.toSemiring.{u2} A _inst_17))))))) (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 (CommRing.toCommSemiring.{u1} R _inst_14)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_14))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_14)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17) _inst_18)))))] [_inst_21 : TopologicalRing.{u2} A _inst_16 (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_17))] [_inst_22 : ContinuousStar.{u2} A _inst_16 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17)) _inst_19)))] [_inst_23 : T2Space.{u2} A _inst_16] (s : StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20), (forall (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) s) (y : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R 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_inst_20) (StarSubalgebra.commRingTopologicalClosure._proof_1.{u1, u2} R A _inst_14 _inst_15 _inst_17 _inst_18 _inst_19 _inst_20) s)) y x)) -> (CommRing.{u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) (StarSubalgebra.topologicalClosure.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 _inst_16 (Ring.toSemiring.{u2} A _inst_17) _inst_18 _inst_19 _inst_20 (StarSubalgebra.commRingTopologicalClosure._proof_2.{u2} A _inst_16 _inst_17 _inst_21) _inst_22 s)))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_14 : CommRing.{u1} R] [_inst_15 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14)))] [_inst_16 : TopologicalSpace.{u2} A] [_inst_17 : Ring.{u2} A] [_inst_18 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17)] [_inst_19 : StarRing.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17))] [_inst_20 : StarModule.{u1, u2} R A (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_14)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14))) _inst_15))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_17))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17)) _inst_19))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17) _inst_18)] [_inst_21 : TopologicalRing.{u2} A _inst_16 (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_17))] [_inst_22 : ContinuousStar.{u2} A _inst_16 (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_17))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17)) _inst_19)))] [_inst_23 : T2Space.{u2} A _inst_16] (s : StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R 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(MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)))) (Subsemiring.toSubmonoid.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)) (Subalgebra.toSubsemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17) _inst_18 (StarSubalgebra.toSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20 s))))) x y) (HMul.hMul.{u2, u2, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (instHMul.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (Submonoid.mul.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)))) (Subsemiring.toSubmonoid.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)) (Subalgebra.toSubsemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17) _inst_18 (StarSubalgebra.toSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20 s))))) y x)) -> (CommRing.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x (StarSubalgebra.topologicalClosure.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 _inst_16 (Ring.toSemiring.{u2} A _inst_17) _inst_18 _inst_19 _inst_20 (TopologicalRing.toTopologicalSemiring.{u2} A _inst_16 (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_17)) _inst_21) _inst_22 s))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_14 : CommRing.{u1} R] [_inst_15 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14)))] [_inst_16 : TopologicalSpace.{u2} A] [_inst_17 : Ring.{u2} A] [_inst_18 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17)] [_inst_19 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17))] [_inst_20 : StarModule.{u1, u2} R A (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_14)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14))) _inst_15))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_17))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)) _inst_19))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17) _inst_18)] [_inst_21 : TopologicalRing.{u2} A _inst_16 (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_17))] [_inst_22 : ContinuousStar.{u2} A _inst_16 (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_17))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)) _inst_19)))] [_inst_23 : T2Space.{u2} A _inst_16] (s : StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20), (forall (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (y : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)), Eq.{succ u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (HMul.hMul.{u2, u2, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (instHMul.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (Submonoid.mul.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)))) (Subsemiring.toSubmonoid.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)) (Subalgebra.toSubsemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17) _inst_18 (StarSubalgebra.toSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20 s))))) x y) (HMul.hMul.{u2, u2, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (instHMul.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x s)) (Submonoid.mul.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)))) (Subsemiring.toSubmonoid.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_17)) (Subalgebra.toSubsemiring.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17) _inst_18 (StarSubalgebra.toSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20 s))))) y x)) -> (CommRing.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) x (StarSubalgebra.topologicalClosure.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 _inst_16 (Ring.toSemiring.{u2} A _inst_17) _inst_18 _inst_19 _inst_20 (TopologicalRing.toTopologicalSemiring.{u2} A _inst_16 (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_17)) _inst_21) _inst_22 s))))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comm_ring_topological_closure StarSubalgebra.commRingTopologicalClosureₓ'. -/
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
@@ -183,7 +183,7 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 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_inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))}, (Continuous.{u1, u3} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u1) (succ u3)} (StarAlgHom.{u2, u1, u3} R 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(StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 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(InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))}, (Continuous.{u1, u3} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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(StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u1) (succ u3)} (StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosureₓ'. -/
 /-- Continuous `star_alg_hom`s from the the topological closure of a `star_subalgebra` whose
 compositions with the `star_subalgebra.inclusion` map agree are, in fact, equal. -/
@@ -212,7 +212,7 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))] {φ : F} {ψ : F}, (Continuous.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (coeFn.{succ u4, max (succ u2) (succ u3)} F (fun (_x : F) => (coeSort.{succ u2, succ (succ u2)} 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_inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A 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 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 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(StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A 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_inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u3} F φ ψ)
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13)))] {φ : F} {ψ : F}, (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A 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(StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u3} F φ ψ)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosureₓ'. -/
 theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : StarSubalgebra R A}
     [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F} (hφ : Continuous φ) (hψ : Continuous ψ)
@@ -315,7 +315,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_6 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_7 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8)))))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_13 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {a : A} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_8 _inst_9 a)))) -> (Eq.{succ u4} F φ ψ)
 but is expected to have type
-  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} 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(elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 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_inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
+  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_13 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {a : A} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12)))] {φ : F} {ψ : F}, (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B 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_inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B 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(StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
 Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_extₓ'. -/
 theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)

19cb3751

bump to nightly-2023-05-03-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

aa7b8e08

Diff

@@ -53,7 +53,7 @@ instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), Embedding.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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(StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
 but is expected to have type
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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 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+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), Embedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 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(Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHomClass.toStarHomClass.{u1, u2, u1, u1} (StarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) 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A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a star subalgebra is an `embedding`. -/
 theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : Embedding (inclusion h) :=
@@ -65,7 +65,7 @@ theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} 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 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h)))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁)) -> (ClosedEmbedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A 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_inst_7)) x S₂)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) 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_inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a closed star subalgebra is a `closed_embedding`. -/
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
@@ -183,7 +183,7 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 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_inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 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(InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))}, (Continuous.{u1, u3} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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(StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))} {ψ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))}, (Continuous.{u1, u3} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 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(StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosureₓ'. -/
 /-- Continuous `star_alg_hom`s from the the topological closure of a `star_subalgebra` whose
 compositions with the `star_subalgebra.inclusion` map agree are, in fact, equal. -/
@@ -212,7 +212,7 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A 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 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13)))] {φ : F} {ψ : F}, (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A 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(StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u3} F φ ψ)
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13)))] {φ : F} {ψ : F}, (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 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 Case conversion may be inaccurate. Consider using '#align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosureₓ'. -/
 theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : StarSubalgebra R A}
     [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F} (hφ : Continuous φ) (hψ : Continuous ψ)
@@ -315,7 +315,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_6 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_7 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8)))))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_13 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {a : A} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A 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_inst_11) _inst_12))) _inst_15))) φ)) -> (Continuous.{u2, u3} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) B (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_3) _inst_10 (coeFn.{succ u4, max (succ 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_inst_8 _inst_9 a)))) -> (Eq.{succ u4} F φ ψ)
 but is expected to have type
-  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_13 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {a : A} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B 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(elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 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_inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ)) -> (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) (Subtype.mk.{succ 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_inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 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(Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) φ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, 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(SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
+  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_13 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {a : A} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ)) -> (Eq.{succ u4} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) (Subtype.mk.{succ 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_inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) φ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
 Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_extₓ'. -/
 theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)

19cb3751

bump to nightly-2023-04-28-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

7fdaed52

Diff

@@ -53,7 +53,7 @@ instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} 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(StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), Embedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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_inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 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(StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a star subalgebra is an `embedding`. -/
 theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : Embedding (inclusion h) :=
@@ -65,7 +65,7 @@ theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) S₁)) -> (ClosedEmbedding.{u2, u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₂) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁) _inst_3) (Subtype.topologicalSpace.{u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₂) _inst_3) (coeFn.{succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) S₁) (coeSort.{succ 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 but is expected to have type
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+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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(StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a closed star subalgebra is a `closed_embedding`. -/
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
@@ -183,7 +183,7 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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_inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B 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_inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))} {ψ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 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_inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) (StarAlgHom.comp.{u2, u1, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A 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_inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) φ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarAlgHom.comp.{u2, u1, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u1) (succ u3)} (StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))))) ψ)) -> (Eq.{max (succ u1) (succ u3)} (StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) (StarAlgHom.comp.{u2, u1, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) φ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarAlgHom.comp.{u2, u1, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) ψ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)))) -> (Eq.{max (succ u1) (succ u3)} (StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosureₓ'. -/
 /-- Continuous `star_alg_hom`s from the the topological closure of a `star_subalgebra` whose
 compositions with the `star_subalgebra.inclusion` map agree are, in fact, equal. -/
@@ -212,7 +212,7 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A 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 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 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+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13)))] {φ : F} {ψ : F}, (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13))) _inst_15)) φ)) -> (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x 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(StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarAlgHomClass.toStarHomClass.{u1, u2, u1, u1} (StarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} 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(StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 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(StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u2, u1, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A 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_inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) x))) -> (Eq.{succ u3} F φ ψ)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosureₓ'. -/
 theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : StarSubalgebra R A}
     [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F} (hφ : Continuous φ) (hψ : Continuous ψ)
@@ -315,7 +315,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_6 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_7 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_8)))))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_13 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {a : A} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 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_inst_8 _inst_9 a)))) -> (Eq.{succ u4} F φ ψ)
 but is expected to have type
-  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} 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_inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 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(Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) φ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, 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(SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
+  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_13 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {a : A} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B 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(StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) φ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
 Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_extₓ'. -/
 theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)

19cb3751

bump to nightly-2023-04-09-02

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

32290448

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
 
 ! This file was ported from Lean 3 source module topology.algebra.star_subalgebra
-! leanprover-community/mathlib commit b7f5a77fa29ad9a3ccc484109b0d7534178e7ecd
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Algebra.Star
 /-!
 # Topological star (sub)algebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A topological star algebra over a topological semiring `R` is a topological semiring with a
 compatible continuous scalar multiplication by elements of `R` and a continuous star operation.
 We reuse typeclass `has_continuous_smul` for topological algebras.

b7f5a77f

bump to nightly-2023-04-07-12

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

77742840

Diff

@@ -46,12 +46,24 @@ instance [TopologicalSpace R] [ContinuousSMul R A] (s : StarSubalgebra R A) : Co
 instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring s :=
   s.toSubalgebra.TopologicalSemiring
 
+/- warning: star_subalgebra.embedding_inclusion -> StarSubalgebra.embedding_inclusion is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A 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(StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S₁ S₂ h))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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+Case conversion may be inaccurate. Consider using '#align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a star subalgebra is an `embedding`. -/
 theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : Embedding (inclusion h) :=
   { induced := Eq.symm induced_compose
     inj := Subtype.map_injective h Function.injective_id }
 #align star_subalgebra.embedding_inclusion StarSubalgebra.embedding_inclusion
 
+/- warning: star_subalgebra.closed_embedding_inclusion -> StarSubalgebra.closedEmbedding_inclusion is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} 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+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A 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_inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) S₁ S₂), (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) S₁)) -> (ClosedEmbedding.{u1, u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A 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+Case conversion may be inaccurate. Consider using '#align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusionₓ'. -/
 /-- The `star_subalgebra.inclusion` of a closed star subalgebra is a `closed_embedding`. -/
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
     (hS₁ : IsClosed (S₁ : Set A)) : ClosedEmbedding (inclusion h) :=
@@ -68,6 +80,7 @@ variable [TopologicalSemiring A] [ContinuousStar A]
 
 variable [TopologicalSpace B] [Semiring B] [Algebra R B] [StarRing B]
 
+#print StarSubalgebra.topologicalClosure /-
 /-- The closure of a star subalgebra in a topological star algebra as a star subalgebra. -/
 def topologicalClosure (s : StarSubalgebra R A) : StarSubalgebra R A :=
   {
@@ -76,17 +89,36 @@ def topologicalClosure (s : StarSubalgebra R A) : StarSubalgebra R A :=
     star_mem' := fun a ha =>
       map_mem_closure continuous_star ha fun x => (star_mem : x ∈ s → star x ∈ s) }
 #align star_subalgebra.topological_closure StarSubalgebra.topologicalClosure
+-/
 
+/- warning: star_subalgebra.topological_closure_coe -> StarSubalgebra.topologicalClosure_coe is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align star_subalgebra.topological_closure_coe StarSubalgebra.topologicalClosure_coeₓ'. -/
 @[simp]
 theorem topologicalClosure_coe (s : StarSubalgebra R A) :
     (s.topologicalClosure : Set A) = closure (s : Set A) :=
   rfl
 #align star_subalgebra.topological_closure_coe StarSubalgebra.topologicalClosure_coe
 
+/- warning: star_subalgebra.le_topological_closure -> StarSubalgebra.le_topologicalClosure is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s)
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.le_topological_closure StarSubalgebra.le_topologicalClosureₓ'. -/
 theorem le_topologicalClosure (s : StarSubalgebra R A) : s ≤ s.topologicalClosure :=
   subset_closure
 #align star_subalgebra.le_topological_closure StarSubalgebra.le_topologicalClosure
 
+/- warning: star_subalgebra.is_closed_topological_closure -> StarSubalgebra.isClosed_topologicalClosure is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] (s : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.is_closed_topological_closure StarSubalgebra.isClosed_topologicalClosureₓ'. -/
 theorem isClosed_topologicalClosure (s : StarSubalgebra R A) :
     IsClosed (s.topologicalClosure : Set A) :=
   isClosed_closure
@@ -97,16 +129,30 @@ instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing
     {S : StarSubalgebra R A} : CompleteSpace S.topologicalClosure :=
   isClosed_closure.completeSpace_coe
 
+/- warning: star_subalgebra.topological_closure_minimal -> StarSubalgebra.topologicalClosure_minimal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] {s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {t : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s t) -> (IsClosed.{u2} A _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)))) t)) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u2} 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+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] {s : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {t : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7}, (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) s t) -> (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) t)) -> (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (OmegaCompletePartialOrder.toPartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_6 _inst_7))))) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s) t)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.topological_closure_minimal StarSubalgebra.topologicalClosure_minimalₓ'. -/
 theorem topologicalClosure_minimal {s t : StarSubalgebra R A} (h : s ≤ t)
     (ht : IsClosed (t : Set A)) : s.topologicalClosure ≤ t :=
   closure_minimal h ht
 #align star_subalgebra.topological_closure_minimal StarSubalgebra.topologicalClosure_minimal
 
+#print StarSubalgebra.topologicalClosure_mono /-
 theorem topologicalClosure_mono : Monotone (topologicalClosure : _ → StarSubalgebra R A) :=
   fun S₁ S₂ h =>
   topologicalClosure_minimal (h.trans <| le_topologicalClosure S₂) (isClosed_topologicalClosure S₂)
 #align star_subalgebra.topological_closure_mono StarSubalgebra.topologicalClosure_mono
+-/
 
+/- warning: star_subalgebra.comm_semiring_topological_closure -> StarSubalgebra.commSemiringTopologicalClosure is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_14 : T2Space.{u2} A _inst_3] (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7), (forall (x : Subtype.{succ u2} A (fun (x : A) => 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_inst_5 _inst_7) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x s)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x s)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x s)) (instHMul.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x s)) (Submonoid.mul.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))) (Subsemiring.toSubmonoid.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 s))))) y x)) -> (CommSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 s))))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.comm_semiring_topological_closure StarSubalgebra.commSemiringTopologicalClosureₓ'. -/
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
 @[reducible]
@@ -115,6 +161,12 @@ def commSemiringTopologicalClosure [T2Space A] (s : StarSubalgebra R A)
   s.toSubalgebra.commSemiringTopologicalClosure hs
 #align star_subalgebra.comm_semiring_topological_closure StarSubalgebra.commSemiringTopologicalClosure
 
+/- warning: star_subalgebra.comm_ring_topological_closure -> StarSubalgebra.commRingTopologicalClosure is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_14 : CommRing.{u1} R] [_inst_15 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14)))] [_inst_16 : TopologicalSpace.{u2} A] [_inst_17 : Ring.{u2} A] [_inst_18 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17)] [_inst_19 : StarRing.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17))] [_inst_20 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R 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_inst_20) (StarSubalgebra.commRingTopologicalClosure._proof_1.{u1, u2} R A _inst_14 _inst_15 _inst_17 _inst_18 _inst_19 _inst_20) s)) y x)) -> (CommRing.{u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 (Ring.toSemiring.{u2} A _inst_17) _inst_19 _inst_18 _inst_20)) (StarSubalgebra.topologicalClosure.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) _inst_15 _inst_16 (Ring.toSemiring.{u2} A _inst_17) _inst_18 _inst_19 _inst_20 (StarSubalgebra.commRingTopologicalClosure._proof_2.{u2} A _inst_16 _inst_17 _inst_21) _inst_22 s)))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_14 : CommRing.{u1} R] [_inst_15 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14)))] [_inst_16 : TopologicalSpace.{u2} A] [_inst_17 : Ring.{u2} A] [_inst_18 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17)] [_inst_19 : StarRing.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17))] [_inst_20 : StarModule.{u1, u2} R A (InvolutiveStar.toStar.{u1} R (StarAddMonoid.toInvolutiveStar.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (Ring.toAddGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_14)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_14))) _inst_15))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_17))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17)) _inst_19))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_14) (Ring.toSemiring.{u2} A _inst_17) _inst_18)] [_inst_21 : TopologicalRing.{u2} A _inst_16 (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_17))] [_inst_22 : ContinuousStar.{u2} A _inst_16 (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_17))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_17)) _inst_19)))] [_inst_23 : T2Space.{u2} A _inst_16] (s : StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R 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(Ring.toSemiring.{u2} A _inst_17) _inst_18 _inst_19 _inst_20 (TopologicalRing.toTopologicalSemiring.{u2} A _inst_16 (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_17)) _inst_21) _inst_22 s))))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.comm_ring_topological_closure StarSubalgebra.commRingTopologicalClosureₓ'. -/
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
 @[reducible]
@@ -124,6 +176,12 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
   s.toSubalgebra.commRingTopologicalClosure hs
 #align star_subalgebra.comm_ring_topological_closure StarSubalgebra.commRingTopologicalClosure
 
+/- warning: star_alg_hom.ext_topological_closure -> StarAlgHom.ext_topologicalClosure is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6))) (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_4)))))) (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_4)))))) (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_4)))))) (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_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_4 _inst_5)))))] [_inst_8 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_9 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u1, u2, u3} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) B _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) A _inst_4 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A 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+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u2, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} {φ : StarAlgHom.{u2, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 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(InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))}, (Continuous.{u1, u3} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13))) φ (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 S (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S) (StarSubalgebra.le_topologicalClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarAlgHom.comp.{u2, u1, u1, u3} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x S)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x 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(StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_13)))) φ ψ)
+Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosureₓ'. -/
 /-- Continuous `star_alg_hom`s from the the topological closure of a `star_subalgebra` whose
 compositions with the `star_subalgebra.inclusion` map agree are, in fact, equal. -/
 theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
@@ -147,6 +205,12 @@ theorem StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
   simpa only using FunLike.congr_fun h x
 #align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosure
 
+/- warning: star_alg_hom_class.ext_topological_closure -> StarAlgHomClass.ext_topologicalClosure is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_7 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A 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(AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u3} B] [_inst_11 : Semiring.{u3} B] [_inst_12 : Algebra.{u1, u3} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)] [_inst_14 : T2Space.{u3} B _inst_10] {F : Type.{u4}} {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u4, u1, u2, u3} F R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) 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+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_6 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_7 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_5)] [_inst_8 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_9 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6)))] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_13 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13)))] {φ : F} {ψ : F}, (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7 (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_6))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_11 _inst_12 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_13))) _inst_15)) φ)) -> (Continuous.{u1, u4} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (instTopologicalSpaceSubtype.{u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7)) x (StarSubalgebra.topologicalClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 S))) B (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_6 _inst_5 _inst_7) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) 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+Case conversion may be inaccurate. Consider using '#align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosureₓ'. -/
 theorem StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _} {S : StarSubalgebra R A}
     [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F} (hφ : Continuous φ) (hψ : Continuous ψ)
     (h :
@@ -176,20 +240,26 @@ variable [ContinuousStar A] [Algebra R A] [StarModule R A]
 
 variable [TopologicalSpace B] [Semiring B] [StarRing B] [Algebra R B]
 
+#print elementalStarAlgebra /-
 /-- The topological closure of the subalgebra generated by a single element. -/
 def elementalStarAlgebra (x : A) : StarSubalgebra R A :=
   (adjoin R ({x} : Set A)).topologicalClosure
 #align elemental_star_algebra elementalStarAlgebra
+-/
 
 namespace elementalStarAlgebra
 
+#print elementalStarAlgebra.self_mem /-
 theorem self_mem (x : A) : x ∈ elementalStarAlgebra R x :=
   SetLike.le_def.mp (le_topologicalClosure _) (self_mem_adjoin_singleton R x)
 #align elemental_star_algebra.self_mem elementalStarAlgebra.self_mem
+-/
 
+#print elementalStarAlgebra.star_self_mem /-
 theorem star_self_mem (x : A) : star x ∈ elementalStarAlgebra R x :=
   star_mem <| self_mem R x
 #align elemental_star_algebra.star_self_mem elementalStarAlgebra.star_self_mem
+-/
 
 /-- The `elemental_star_algebra` generated by a normal element is commutative. -/
 instance [T2Space A] {x : A} [IsStarNormal x] : CommSemiring (elementalStarAlgebra R x) :=
@@ -201,20 +271,29 @@ instance {R A} [CommRing R] [StarRing R] [TopologicalSpace A] [Ring A] [Algebra
     CommRing (elementalStarAlgebra R x) :=
   StarSubalgebra.commRingTopologicalClosure _ mul_comm
 
+#print elementalStarAlgebra.isClosed /-
 protected theorem isClosed (x : A) : IsClosed (elementalStarAlgebra R x : Set A) :=
   isClosed_closure
 #align elemental_star_algebra.is_closed elementalStarAlgebra.isClosed
+-/
 
 instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing A]
     [TopologicalSemiring A] [ContinuousStar A] [Algebra R A] [StarModule R A] (x : A) :
     CompleteSpace (elementalStarAlgebra R x) :=
   isClosed_closure.completeSpace_coe
 
+/- warning: elemental_star_algebra.le_of_is_closed_of_mem -> elementalStarAlgebra.le_of_isClosed_of_mem is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_6 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_7 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u1, u2} R A (InvolutiveStar.toHasStar.{u1} 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(forall {x : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x S) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteSemilatticeInf.toPartialOrder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteLattice.toCompleteSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_8 _inst_5 _inst_9))))) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 x) S))
+but is expected to have type
+  forall (R : Type.{u2}) {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9}, (IsClosed.{u1} A _inst_3 (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) S)) -> (forall {x : A}, (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x S) -> (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (OmegaCompletePartialOrder.toPartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_8 _inst_5 _inst_9))))) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 x) S))
+Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.le_of_is_closed_of_mem elementalStarAlgebra.le_of_isClosed_of_memₓ'. -/
 theorem le_of_isClosed_of_mem {S : StarSubalgebra R A} (hS : IsClosed (S : Set A)) {x : A}
     (hx : x ∈ S) : elementalStarAlgebra R x ≤ S :=
   topologicalClosure_minimal (adjoin_le <| Set.singleton_subset_iff.2 hx) hS
 #align elemental_star_algebra.le_of_is_closed_of_mem elementalStarAlgebra.le_of_isClosed_of_mem
 
+#print elementalStarAlgebra.closedEmbedding_coe /-
 /-- The coercion from an elemental algebra to the full algebra as a `closed_embedding`. -/
 theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebra R x → A) :=
   { induced := rfl
@@ -227,7 +306,14 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding (coe : elementalStarAlgebr
             rintro ⟨y, rfl⟩
             exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩ }
 #align elemental_star_algebra.closed_embedding_coe elementalStarAlgebra.closedEmbedding_coe
+-/
 
+/- warning: elemental_star_algebra.star_alg_hom_class_ext -> elementalStarAlgebra.starAlgHomClass_ext is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : TopologicalSpace.{u2} A] [_inst_4 : Semiring.{u2} A] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)] [_inst_6 : TopologicalSemiring.{u2} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_4))] [_inst_7 : ContinuousStar.{u2} A _inst_3 (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u1, u2} R A 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_inst_8 _inst_9) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toHasStar.{u2} A (StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toHasStar.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_11) _inst_12))) _inst_15))) ψ (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u4} F φ ψ)
+but is expected to have type
+  forall (R : Type.{u2}) {A : Type.{u1}} {B : Type.{u4}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : TopologicalSpace.{u1} A] [_inst_4 : Semiring.{u1} A] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4)] [_inst_6 : TopologicalSemiring.{u1} A _inst_3 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4))] [_inst_7 : ContinuousStar.{u1} A _inst_3 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5)))] [_inst_8 : Algebra.{u2, u1} R A _inst_1 _inst_4] [_inst_9 : StarModule.{u2, u1} R A (InvolutiveStar.toStar.{u2} R (StarAddMonoid.toInvolutiveStar.{u2} R (AddMonoidWithOne.toAddMonoid.{u2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_4 _inst_8)] [_inst_10 : TopologicalSpace.{u4} B] [_inst_11 : Semiring.{u4} B] [_inst_12 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11)] [_inst_13 : Algebra.{u2, u4} R B _inst_1 _inst_11] [_inst_14 : T2Space.{u4} B _inst_10] {F : Type.{u3}} {a : A} [_inst_15 : StarAlgHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 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(elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_3) _inst_10 (FunLike.coe.{succ u3, succ u1, succ u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (fun (_x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) => B) _x) (StarHomClass.toFunLike.{u3, u1, u4} F (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 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_inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) (StarAlgHomClass.toStarHomClass.{u3, u2, u1, u4} F R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) B _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_4 _inst_8 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a))) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9 (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_4)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_4) _inst_5))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) _inst_11 _inst_13 (InvolutiveStar.toStar.{u4} B (StarAddMonoid.toInvolutiveStar.{u4} B (AddMonoidWithOne.toAddMonoid.{u4} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} B (NonAssocSemiring.toAddCommMonoidWithOne.{u4} B (Semiring.toNonAssocSemiring.{u4} B _inst_11)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_11) _inst_12))) _inst_15)) ψ (Subtype.mk.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_4 _inst_5 _inst_8 _inst_9)) x (elementalStarAlgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)) a (elementalStarAlgebra.self_mem.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 a)))) -> (Eq.{succ u3} F φ ψ)
+Case conversion may be inaccurate. Consider using '#align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_extₓ'. -/
 theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)
     (hψ : Continuous ψ) (h : φ ⟨a, self_mem R a⟩ = ψ ⟨a, self_mem R a⟩) : φ = ψ :=

b7f5a77f

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -59,7 +59,7 @@ theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤
     closed_range :=
       isClosed_induced_iff.2
         ⟨S₁, hS₁, by
-          convert (Set.range_subtype_map id _).symm
+          convert(Set.range_subtype_map id _).symm
           rw [Set.image_id]
           rfl⟩ }
 #align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusion

b7f5a77f

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

b7f5a77f

feat: add induction principle for elementalStarAlgebra (#12039)

61447777

Diff

@@ -218,7 +218,7 @@ instance {R A} [CommRing R] [StarRing R] [TopologicalSpace A] [Ring A] [Algebra
     CommRing (elementalStarAlgebra R x) :=
   StarSubalgebra.commRingTopologicalClosure _ mul_comm
 
-protected theorem isClosed (x : A) : IsClosed (elementalStarAlgebra R x : Set A) :=
+theorem isClosed (x : A) : IsClosed (elementalStarAlgebra R x : Set A) :=
   isClosed_closure
 #align elemental_star_algebra.is_closed elementalStarAlgebra.isClosed
 
@@ -237,7 +237,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding ((↑) : elementalStarAlge
   { induced := rfl
     inj := Subtype.coe_injective
     isClosed_range := by
-      convert elementalStarAlgebra.isClosed R x
+      convert isClosed R x
       exact
         Set.ext fun y =>
           ⟨by
@@ -245,6 +245,30 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding ((↑) : elementalStarAlge
             exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩ }
 #align elemental_star_algebra.closed_embedding_coe elementalStarAlgebra.closedEmbedding_coe
 
+@[elab_as_elim]
+theorem induction_on {x y : A}
+    (hy : y ∈ elementalStarAlgebra R x) {P : (u : A) → u ∈ elementalStarAlgebra R x → Prop}
+    (self : P x (self_mem R x)) (star_self : P (star x) (star_self_mem R x))
+    (algebraMap : ∀ r, P (algebraMap R A r) (_root_.algebraMap_mem _ r))
+    (add : ∀ u hu v hv, P u hu → P v hv → P (u + v) (add_mem hu hv))
+    (mul : ∀ u hu v hv, P u hu → P v hv → P (u * v) (mul_mem hu hv))
+    (closure : ∀ s : Set A, (hs : s ⊆ elementalStarAlgebra R x) → (∀ u, (hu : u ∈ s) →
+      P u (hs hu)) → ∀ v, (hv : v ∈ closure s) → P v (closure_minimal hs (isClosed R x) hv)) :
+    P y hy := by
+  apply closure (adjoin R {x} : Set A) subset_closure (fun y hy ↦ ?_) y hy
+  rw [SetLike.mem_coe, ← mem_toSubalgebra, adjoin_toSubalgebra] at hy
+  induction hy using Algebra.adjoin_induction'' with
+  | mem u hu =>
+    obtain ((rfl : u = x) | (hu : star u = x)) := by simpa using hu
+    · exact self
+    · simp_rw [← hu, star_star] at star_self
+      exact star_self
+  | algebraMap r => exact algebraMap r
+  | add u hu_mem v hv_mem hu hv =>
+    exact add u (subset_closure hu_mem) v (subset_closure hv_mem) (hu hu_mem) (hv hv_mem)
+  | mul u hu_mem v hv_mem hu hv =>
+    exact mul u (subset_closure hu_mem) v (subset_closure hv_mem) (hu hu_mem) (hv hv_mem)
+
 theorem starAlgHomClass_ext [T2Space B] {F : Type*} {a : A}
     [FunLike F (elementalStarAlgebra R a) B] [AlgHomClass F R _ B] [StarAlgHomClass F R _ B]
     {φ ψ : F} (hφ : Continuous φ)

b7f5a77f

chore: rename StarSubalgebra.adjoin to StarAlgebra.adjoin (#11339)

This makes it consistent with all the other adjoin in the library

2b6a6f13

Diff

@@ -185,7 +185,7 @@ end StarSubalgebra
 
 section Elemental
 
-open StarSubalgebra
+open StarSubalgebra StarAlgebra
 
 variable (R : Type*) {A B : Type*} [CommSemiring R] [StarRing R]
 variable [TopologicalSpace A] [Semiring A] [StarRing A] [TopologicalSemiring A]

b7f5a77f

chore: rename open_range to isOpen_range, closed_range to isClosed_range (#11438)

All these lemmas refer to the range of some function being open/range (i.e. isOpen or isClosed).

75784e0d

Diff

@@ -50,7 +50,7 @@ theorem embedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
     (hS₁ : IsClosed (S₁ : Set A)) : ClosedEmbedding (inclusion h) :=
   { embedding_inclusion h with
-    closed_range := isClosed_induced_iff.2
+    isClosed_range := isClosed_induced_iff.2
       ⟨S₁, hS₁, by
           convert (Set.range_subtype_map id _).symm
           · rw [Set.image_id]; rfl
@@ -236,7 +236,7 @@ theorem le_of_isClosed_of_mem {S : StarSubalgebra R A} (hS : IsClosed (S : Set A
 theorem closedEmbedding_coe (x : A) : ClosedEmbedding ((↑) : elementalStarAlgebra R x → A) :=
   { induced := rfl
     inj := Subtype.coe_injective
-    closed_range := by
+    isClosed_range := by
       convert elementalStarAlgebra.isClosed R x
       exact
         Set.ext fun y =>

b7f5a77f

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -35,7 +35,6 @@ namespace StarSubalgebra
 section TopologicalStarAlgebra
 
 variable {R A B : Type*} [CommSemiring R] [StarRing R]
-
 variable [TopologicalSpace A] [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
 
 instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring s :=
@@ -60,7 +59,6 @@ theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤
 #align star_subalgebra.closed_embedding_inclusion StarSubalgebra.closedEmbedding_inclusion
 
 variable [TopologicalSemiring A] [ContinuousStar A]
-
 variable [TopologicalSpace B] [Semiring B] [Algebra R B] [StarRing B]
 
 /-- The closure of a star subalgebra in a topological star algebra as a star subalgebra. -/
@@ -190,11 +188,8 @@ section Elemental
 open StarSubalgebra
 
 variable (R : Type*) {A B : Type*} [CommSemiring R] [StarRing R]
-
 variable [TopologicalSpace A] [Semiring A] [StarRing A] [TopologicalSemiring A]
-
 variable [ContinuousStar A] [Algebra R A] [StarModule R A]
-
 variable [TopologicalSpace B] [Semiring B] [StarRing B] [Algebra R B]
 
 /-- The topological closure of the subalgebra generated by a single element. -/

b7f5a77f

chore: scope open Classical (#11199)

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

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

c747be0a

Diff

@@ -25,9 +25,10 @@ which as a star algebra is a topological star algebra.
 -/
 
 
-open Classical Set TopologicalSpace
+open scoped Classical
+open Set TopologicalSpace
 
-open Classical
+open scoped Classical
 
 namespace StarSubalgebra

b7f5a77f

chore: add missing elab_as_elim (#11061)

Dependent induction did not support this attribute in Lean 3.

A few downstream applys change to refine as a result. A future PR could replace some of these with induction.

92c93d7c

Diff

@@ -257,7 +257,7 @@ theorem starAlgHomClass_ext [T2Space B] {F : Type*} {a : A}
   have : StarAlgHomClass F R (↥(topologicalClosure (adjoin R {a}))) B :=
     inferInstanceAs (StarAlgHomClass F R (elementalStarAlgebra R a) B)
   refine StarAlgHomClass.ext_topologicalClosure hφ hψ fun x => ?_
-  apply adjoin_induction' x ?_ ?_ ?_ ?_ ?_
+  refine adjoin_induction' x ?_ ?_ ?_ ?_ ?_
   exacts [fun y hy => by simpa only [Set.mem_singleton_iff.mp hy] using h, fun r => by
     simp only [AlgHomClass.commutes], fun x y hx hy => by simp only [map_add, hx, hy],
     fun x y hx hy => by simp only [map_mul, hx, hy], fun x hx => by simp only [map_star, hx]]

b7f5a77f

chore: bump aesop; update syntax (#10955)

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

46974e92

Diff

@@ -203,7 +203,7 @@ def elementalStarAlgebra (x : A) : StarSubalgebra R A :=
 
 namespace elementalStarAlgebra
 
-@[aesop safe apply (rule_sets [SetLike])]
+@[aesop safe apply (rule_sets := [SetLike])]
 theorem self_mem (x : A) : x ∈ elementalStarAlgebra R x :=
   SetLike.le_def.mp (le_topologicalClosure _) (self_mem_adjoin_singleton R x)
 #align elemental_star_algebra.self_mem elementalStarAlgebra.self_mem

b7f5a77f

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -167,7 +167,8 @@ theorem _root_.StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra
 #align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosure
 
 theorem _root_.StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type*}
-    {S : StarSubalgebra R A} [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F}
+    {S : StarSubalgebra R A} [FunLike F S.topologicalClosure B]
+    [AlgHomClass F R S.topologicalClosure B] [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F}
     (hφ : Continuous φ) (hψ : Continuous ψ) (h : ∀ x : S,
         φ (inclusion (le_topologicalClosure S) x) = ψ ((inclusion (le_topologicalClosure S)) x)) :
     φ = ψ := by
@@ -249,8 +250,12 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding ((↑) : elementalStarAlge
 #align elemental_star_algebra.closed_embedding_coe elementalStarAlgebra.closedEmbedding_coe
 
 theorem starAlgHomClass_ext [T2Space B] {F : Type*} {a : A}
-    [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)
+    [FunLike F (elementalStarAlgebra R a) B] [AlgHomClass F R _ B] [StarAlgHomClass F R _ B]
+    {φ ψ : F} (hφ : Continuous φ)
     (hψ : Continuous ψ) (h : φ ⟨a, self_mem R a⟩ = ψ ⟨a, self_mem R a⟩) : φ = ψ := by
+  -- Note: help with unfolding `elementalStarAlgebra`
+  have : StarAlgHomClass F R (↥(topologicalClosure (adjoin R {a}))) B :=
+    inferInstanceAs (StarAlgHomClass F R (elementalStarAlgebra R a) B)
   refine StarAlgHomClass.ext_topologicalClosure hφ hψ fun x => ?_
   apply adjoin_induction' x ?_ ?_ ?_ ?_ ?_
   exacts [fun y hy => by simpa only [Set.mem_singleton_iff.mp hy] using h, fun r => by

b7f5a77f

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

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

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

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

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

82656743

Diff

@@ -151,7 +151,7 @@ theorem _root_.StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra
     (h :
       φ.comp (inclusion (le_topologicalClosure S)) = ψ.comp (inclusion (le_topologicalClosure S))) :
     φ = ψ := by
-  rw [FunLike.ext'_iff]
+  rw [DFunLike.ext'_iff]
   have : Dense (Set.range <| inclusion (le_topologicalClosure S)) := by
     refine' embedding_subtype_val.toInducing.dense_iff.2 fun x => _
     convert show ↑x ∈ closure (S : Set A) from x.prop
@@ -163,7 +163,7 @@ theorem _root_.StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra
           exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩
   refine' Continuous.ext_on this hφ hψ _
   rintro _ ⟨x, rfl⟩
-  simpa only using FunLike.congr_fun h x
+  simpa only using DFunLike.congr_fun h x
 #align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosure
 
 theorem _root_.StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type*}
@@ -175,7 +175,7 @@ theorem _root_.StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type*}
   have : (φ : S.topologicalClosure →⋆ₐ[R] B) = (ψ : S.topologicalClosure →⋆ₐ[R] B) := by
     refine StarAlgHom.ext_topologicalClosure (R := R) (A := A) (B := B) hφ hψ (StarAlgHom.ext ?_)
     simpa only [StarAlgHom.coe_comp, StarAlgHom.coe_coe] using h
-  rw [FunLike.ext'_iff, ← StarAlgHom.coe_coe]
+  rw [DFunLike.ext'_iff, ← StarAlgHom.coe_coe]
   apply congrArg _ this
 #align star_alg_hom_class.ext_topological_closure StarAlgHomClass.ext_topologicalClosure

b7f5a77f

feat: add Inducing.continuousSMul (#9713)

add Inducing.continuousSMul and Inducing.continuousVAdd;
use it to golf Units.continuousSMul and Inducing.continuousMul;
generalize Submonoid.continuousSMul from a submonoid of a group to a submonoid of a monoid;
reuse Submonoid.continuousSMul in Subgroup.continuousSMul.

350879f7

Diff

@@ -37,9 +37,6 @@ variable {R A B : Type*} [CommSemiring R] [StarRing R]
 
 variable [TopologicalSpace A] [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
 
-instance [TopologicalSpace R] [ContinuousSMul R A] (s : StarSubalgebra R A) : ContinuousSMul R s :=
-  s.toSubalgebra.continuousSMul
-
 instance [TopologicalSemiring A] (s : StarSubalgebra R A) : TopologicalSemiring s :=
   s.toSubalgebra.topologicalSemiring

b7f5a77f

feat: add a SetLike default rule set for aesop (#7111)

This creates a new aesop rule set called SetLike to house lemmas about membership in subobjects.

Lemmas like pow_mem should be included in the rule set:

@[to_additive (attr := aesop safe apply (rule_sets [SetLike]))]
theorem pow_mem {M A} [Monoid M] [SetLike A M] [SubmonoidClass A M] {S : A} {x : M}
(hx : x ∈ S) : ∀ n : ℕ, x ^ n ∈ S

Lemmas about closures, like AddSubmonoid.closure should be included in the rule set, but they should be assigned a penalty (here we choose 20 throughout) so that they are not attempted before the general purpose ones like pow_mem.

@[to_additive (attr := simp, aesop safe 20 apply (rule_sets [SetLike]))
  "The `AddSubmonoid` generated by a set includes the set."]
theorem subset_closure : s ⊆ closure s := fun _ hx => mem_closure.2 fun _ hS => hS hx

In order for aesop to make effective use of AddSubmonoid.closure it needs the following new lemma.

@[aesop 5% apply (rule_sets [SetLike])]
lemma mem_of_subset {s : Set B} (hp : s ⊆ p) {x : B} (hx : x ∈ s) : x ∈ p := hp hx

Note: this lemma is marked as very unsafe (5%) because it will apply whenever the goal is of the form x ∈ p where p is any term of a SetLike instance; and moreover, it will create s as a metavariable, which is in general a terrible idea, but necessary for the reason mentioned above.

214e72fd

Diff

@@ -205,6 +205,7 @@ def elementalStarAlgebra (x : A) : StarSubalgebra R A :=
 
 namespace elementalStarAlgebra
 
+@[aesop safe apply (rule_sets [SetLike])]
 theorem self_mem (x : A) : x ∈ elementalStarAlgebra R x :=
   SetLike.le_def.mp (le_topologicalClosure _) (self_mem_adjoin_singleton R x)
 #align elemental_star_algebra.self_mem elementalStarAlgebra.self_mem

b7f5a77f

chore: missing spaces after rcases, convert and congrm (#7725)

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

c5594244

Diff

@@ -55,7 +55,7 @@ theorem closedEmbedding_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤
   { embedding_inclusion h with
     closed_range := isClosed_induced_iff.2
       ⟨S₁, hS₁, by
-          convert(Set.range_subtype_map id _).symm
+          convert (Set.range_subtype_map id _).symm
           · rw [Set.image_id]; rfl
           · intro _ h'
             apply h h' ⟩ }

b7f5a77f

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

@@ -33,7 +33,7 @@ namespace StarSubalgebra
 
 section TopologicalStarAlgebra
 
-variable {R A B : Type _} [CommSemiring R] [StarRing R]
+variable {R A B : Type*} [CommSemiring R] [StarRing R]
 
 variable [TopologicalSpace A] [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
 
@@ -93,7 +93,7 @@ theorem isClosed_topologicalClosure (s : StarSubalgebra R A) :
   isClosed_closure
 #align star_subalgebra.is_closed_topological_closure StarSubalgebra.isClosed_topologicalClosure
 
-instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing A]
+instance {A : Type*} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing A]
     [TopologicalSemiring A] [ContinuousStar A] [Algebra R A] [StarModule R A]
     {S : StarSubalgebra R A} : CompleteSpace S.topologicalClosure :=
   isClosed_closure.completeSpace_coe
@@ -169,7 +169,7 @@ theorem _root_.StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra
   simpa only using FunLike.congr_fun h x
 #align star_alg_hom.ext_topological_closure StarAlgHom.ext_topologicalClosure
 
-theorem _root_.StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type _}
+theorem _root_.StarAlgHomClass.ext_topologicalClosure [T2Space B] {F : Type*}
     {S : StarSubalgebra R A} [StarAlgHomClass F R S.topologicalClosure B] {φ ψ : F}
     (hφ : Continuous φ) (hψ : Continuous ψ) (h : ∀ x : S,
         φ (inclusion (le_topologicalClosure S) x) = ψ ((inclusion (le_topologicalClosure S)) x)) :
@@ -190,7 +190,7 @@ section Elemental
 
 open StarSubalgebra
 
-variable (R : Type _) {A B : Type _} [CommSemiring R] [StarRing R]
+variable (R : Type*) {A B : Type*} [CommSemiring R] [StarRing R]
 
 variable [TopologicalSpace A] [Semiring A] [StarRing A] [TopologicalSemiring A]
 
@@ -227,7 +227,7 @@ protected theorem isClosed (x : A) : IsClosed (elementalStarAlgebra R x : Set A)
   isClosed_closure
 #align elemental_star_algebra.is_closed elementalStarAlgebra.isClosed
 
-instance {A : Type _} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing A]
+instance {A : Type*} [UniformSpace A] [CompleteSpace A] [Semiring A] [StarRing A]
     [TopologicalSemiring A] [ContinuousStar A] [Algebra R A] [StarModule R A] (x : A) :
     CompleteSpace (elementalStarAlgebra R x) :=
   isClosed_closure.completeSpace_coe
@@ -250,7 +250,7 @@ theorem closedEmbedding_coe (x : A) : ClosedEmbedding ((↑) : elementalStarAlge
             exact y.prop, fun hy => ⟨⟨y, hy⟩, rfl⟩⟩ }
 #align elemental_star_algebra.closed_embedding_coe elementalStarAlgebra.closedEmbedding_coe
 
-theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
+theorem starAlgHomClass_ext [T2Space B] {F : Type*} {a : A}
     [StarAlgHomClass F R (elementalStarAlgebra R a) B] {φ ψ : F} (hφ : Continuous φ)
     (hψ : Continuous ψ) (h : φ ⟨a, self_mem R a⟩ = ψ ⟨a, self_mem R a⟩) : φ = ψ := by
   refine StarAlgHomClass.ext_topologicalClosure hφ hψ fun x => ?_

b7f5a77f

refactor: link the Stone-Weierstrass theorem to the StarSubalgebra API (#5267)

The Stone-Weierstrass theorem, including the version for IsROrC 𝕜, was developed prior to the introduction of StarSubalgebra. As such, in order to prove it, a predicate ConjInvariantSubalgebra was introduced for ℝ-subalgebras of C(X, 𝕜). This refactors the Stone-Weierstrass theorem to instead use the StarSubalgebra API and removes ContinuousMap.ConjInvariantSubalgebra entirely. In addition, we provide a few corollaries concerning polynomial functions which are missing from the library.

6220e1d0

Diff

@@ -74,6 +74,10 @@ def topologicalClosure (s : StarSubalgebra R A) : StarSubalgebra R A :=
       map_mem_closure continuous_star ha fun x => (star_mem : x ∈ s → star x ∈ s) }
 #align star_subalgebra.topological_closure StarSubalgebra.topologicalClosure
 
+theorem topologicalClosure_toSubalgebra_comm (s : StarSubalgebra R A) :
+    s.topologicalClosure.toSubalgebra = s.toSubalgebra.topologicalClosure :=
+  SetLike.coe_injective rfl
+
 @[simp]
 theorem topologicalClosure_coe (s : StarSubalgebra R A) :
     (s.topologicalClosure : Set A) = closure (s : Set A) :=
@@ -119,6 +123,13 @@ theorem topologicalClosure_map [StarModule R B] [TopologicalSemiring B] [Continu
     (map φ s).topologicalClosure = map φ s.topologicalClosure :=
   SetLike.coe_injective <| hφ.closure_image_eq _
 
+theorem _root_.Subalgebra.topologicalClosure_star_comm (s : Subalgebra R A) :
+    (star s).topologicalClosure = star s.topologicalClosure := by
+  suffices ∀ t : Subalgebra R A, (star t).topologicalClosure ≤ star t.topologicalClosure from
+    le_antisymm (this s) (by simpa only [star_star] using Subalgebra.star_mono (this (star s)))
+  exact fun t => (star t).topologicalClosure_minimal (Subalgebra.star_mono subset_closure)
+    (isClosed_closure.preimage continuous_star)
+
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
 @[reducible]

b7f5a77f

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Jireh Loreaux. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jireh Loreaux
-
-! This file was ported from Lean 3 source module topology.algebra.star_subalgebra
-! leanprover-community/mathlib commit b7f5a77fa29ad9a3ccc484109b0d7534178e7ecd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Star.Subalgebra
 import Mathlib.Topology.Algebra.Algebra
 import Mathlib.Topology.Algebra.Star
 
+#align_import topology.algebra.star_subalgebra from "leanprover-community/mathlib"@"b7f5a77fa29ad9a3ccc484109b0d7534178e7ecd"
+
 /-!
 # Topological star (sub)algebras

b7f5a77f

feat: interaction between StarSubalgebra.map and topologicalClosure (#5166)

ab415df4

Diff

@@ -107,6 +107,21 @@ theorem topologicalClosure_mono : Monotone (topologicalClosure : _ → StarSubal
   topologicalClosure_minimal (h.trans <| le_topologicalClosure S₂) (isClosed_topologicalClosure S₂)
 #align star_subalgebra.topological_closure_mono StarSubalgebra.topologicalClosure_mono
 
+theorem topologicalClosure_map_le [StarModule R B] [TopologicalSemiring B] [ContinuousStar B]
+    (s : StarSubalgebra R A) (φ : A →⋆ₐ[R] B) (hφ : IsClosedMap φ) :
+    (map φ s).topologicalClosure ≤ map φ s.topologicalClosure :=
+  hφ.closure_image_subset _
+
+theorem map_topologicalClosure_le [StarModule R B] [TopologicalSemiring B] [ContinuousStar B]
+    (s : StarSubalgebra R A) (φ : A →⋆ₐ[R] B) (hφ : Continuous φ) :
+    map φ s.topologicalClosure ≤ (map φ s).topologicalClosure :=
+  image_closure_subset_closure_image hφ
+
+theorem topologicalClosure_map [StarModule R B] [TopologicalSemiring B] [ContinuousStar B]
+    (s : StarSubalgebra R A) (φ : A →⋆ₐ[R] B) (hφ : ClosedEmbedding φ) :
+    (map φ s).topologicalClosure = map φ s.topologicalClosure :=
+  SetLike.coe_injective <| hφ.closure_image_eq _
+
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
 @[reducible]

b7f5a77f

chore: fix many typos (#4983)

These are all doc fixes

54b72114

Diff

@@ -124,7 +124,7 @@ def commRingTopologicalClosure {R A} [CommRing R] [StarRing R] [TopologicalSpace
   s.toSubalgebra.commRingTopologicalClosure hs
 #align star_subalgebra.comm_ring_topological_closure StarSubalgebra.commRingTopologicalClosure
 
-/-- Continuous `StarAlgHom`s from the the topological closure of a `StarSubalgebra` whose
+/-- Continuous `StarAlgHom`s from the topological closure of a `StarSubalgebra` whose
 compositions with the `StarSubalgebra.inclusion` map agree are, in fact, equal. -/
 theorem _root_.StarAlgHom.ext_topologicalClosure [T2Space B] {S : StarSubalgebra R A}
     {φ ψ : S.topologicalClosure →⋆ₐ[R] B} (hφ : Continuous φ) (hψ : Continuous ψ)

b7f5a77f

chore: add space after exacts (#4945)

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

bf799bb9

Diff

@@ -232,7 +232,7 @@ theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
     (hψ : Continuous ψ) (h : φ ⟨a, self_mem R a⟩ = ψ ⟨a, self_mem R a⟩) : φ = ψ := by
   refine StarAlgHomClass.ext_topologicalClosure hφ hψ fun x => ?_
   apply adjoin_induction' x ?_ ?_ ?_ ?_ ?_
-  exacts[fun y hy => by simpa only [Set.mem_singleton_iff.mp hy] using h, fun r => by
+  exacts [fun y hy => by simpa only [Set.mem_singleton_iff.mp hy] using h, fun r => by
     simp only [AlgHomClass.commutes], fun x y hx hy => by simp only [map_add, hx, hy],
     fun x y hx hy => by simp only [map_mul, hx, hy], fun x hx => by simp only [map_star, hx]]
 #align elemental_star_algebra.star_alg_hom_class_ext elementalStarAlgebra.starAlgHomClass_ext

b7f5a77f

chore: fix upper/lowercase in comments (#4360)

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

27d257fc

Diff

@@ -17,7 +17,7 @@ import Mathlib.Topology.Algebra.Star
 
 A topological star algebra over a topological semiring `R` is a topological semiring with a
 compatible continuous scalar multiplication by elements of `R` and a continuous star operation.
-We reuse typeclass `has_continuous_smul` for topological algebras.
+We reuse typeclass `ContinuousSMul` for topological algebras.
 
 ## Results

b7f5a77f

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -115,8 +115,6 @@ def commSemiringTopologicalClosure [T2Space A] (s : StarSubalgebra R A)
   s.toSubalgebra.commSemiringTopologicalClosure hs
 #align star_subalgebra.comm_semiring_topological_closure StarSubalgebra.commSemiringTopologicalClosure
 
--- Porting note: could not synth StarRing
-set_option synthInstance.etaExperiment true in
 /-- If a star subalgebra of a topological star algebra is commutative, then so is its topological
 closure. See note [reducible non-instances]. -/
 @[reducible]
@@ -196,8 +194,6 @@ theorem star_self_mem (x : A) : star x ∈ elementalStarAlgebra R x :=
 instance [T2Space A] {x : A} [IsStarNormal x] : CommSemiring (elementalStarAlgebra R x) :=
   StarSubalgebra.commSemiringTopologicalClosure _ mul_comm
 
--- Porting note: could not synth StarRing
-set_option synthInstance.etaExperiment true in
 /-- The `elementalStarAlgebra` generated by a normal element is commutative. -/
 instance {R A} [CommRing R] [StarRing R] [TopologicalSpace A] [Ring A] [Algebra R A] [StarRing A]
     [StarModule R A] [TopologicalRing A] [ContinuousStar A] [T2Space A] {x : A} [IsStarNormal x] :
@@ -244,4 +240,3 @@ theorem starAlgHomClass_ext [T2Space B] {F : Type _} {a : A}
 end elementalStarAlgebra
 
 end Elemental
-

b7f5a77f

feat: port Topology.Algebra.StarSubalgebra (#3319)

e39b2102

`topology.algebra.star_subalgebra` ⟷ `Mathlib.Topology.Algebra.StarSubalgebra`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 9 + 530

topology.algebra.star_subalgebra ⟷ Mathlib.Topology.Algebra.StarSubalgebra

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 9 + 530

`topology.algebra.star_subalgebra` ⟷ `Mathlib.Topology.Algebra.StarSubalgebra`

`simp` not firing sometimes