algebra.star.subalgebra ⟷ Mathlib.Algebra.Star.Subalgebra

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

@@ -531,7 +531,7 @@ variable [Semiring B] [Algebra R B] [StarRing B] [StarModule R B]
 
 variable (R)
 
-#print StarSubalgebra.adjoin /-
+#print StarAlgebra.adjoin /-
 /-- The minimal star subalgebra that contains `s`. -/
 @[simps]
 def adjoin (s : Set A) : StarSubalgebra R A :=
@@ -539,51 +539,51 @@ def adjoin (s : Set A) : StarSubalgebra R A :=
     star_mem' := fun x hx => by
       rwa [Subalgebra.mem_carrier, ← Subalgebra.mem_star_iff, Subalgebra.star_adjoin_comm,
         Set.union_star, star_star, Set.union_comm] }
-#align star_subalgebra.adjoin StarSubalgebra.adjoin
+#align star_subalgebra.adjoin StarAlgebra.adjoin
 -/
 
-#print StarSubalgebra.adjoin_eq_starClosure_adjoin /-
+#print StarAlgebra.adjoin_eq_starClosure_adjoin /-
 theorem adjoin_eq_starClosure_adjoin (s : Set A) : adjoin R s = (Algebra.adjoin R s).starClosure :=
   toSubalgebra_injective <|
     show Algebra.adjoin R (s ∪ star s) = Algebra.adjoin R s ⊔ star (Algebra.adjoin R s) from
       (Subalgebra.star_adjoin_comm R s).symm ▸ Algebra.adjoin_union s (star s)
-#align star_subalgebra.adjoin_eq_star_closure_adjoin StarSubalgebra.adjoin_eq_starClosure_adjoin
+#align star_subalgebra.adjoin_eq_star_closure_adjoin StarAlgebra.adjoin_eq_starClosure_adjoin
 -/
 
-#print StarSubalgebra.adjoin_toSubalgebra /-
+#print StarAlgebra.adjoin_toSubalgebra /-
 theorem adjoin_toSubalgebra (s : Set A) :
     (adjoin R s).toSubalgebra = Algebra.adjoin R (s ∪ star s) :=
   rfl
-#align star_subalgebra.adjoin_to_subalgebra StarSubalgebra.adjoin_toSubalgebra
+#align star_subalgebra.adjoin_to_subalgebra StarAlgebra.adjoin_toSubalgebra
 -/
 
-#print StarSubalgebra.subset_adjoin /-
+#print StarAlgebra.subset_adjoin /-
 theorem subset_adjoin (s : Set A) : s ⊆ adjoin R s :=
   (Set.subset_union_left s (star s)).trans Algebra.subset_adjoin
-#align star_subalgebra.subset_adjoin StarSubalgebra.subset_adjoin
+#align star_subalgebra.subset_adjoin StarAlgebra.subset_adjoin
 -/
 
-#print StarSubalgebra.star_subset_adjoin /-
+#print StarAlgebra.star_subset_adjoin /-
 theorem star_subset_adjoin (s : Set A) : star s ⊆ adjoin R s :=
   (Set.subset_union_right s (star s)).trans Algebra.subset_adjoin
-#align star_subalgebra.star_subset_adjoin StarSubalgebra.star_subset_adjoin
+#align star_subalgebra.star_subset_adjoin StarAlgebra.star_subset_adjoin
 -/
 
-#print StarSubalgebra.self_mem_adjoin_singleton /-
+#print StarAlgebra.self_mem_adjoin_singleton /-
 theorem self_mem_adjoin_singleton (x : A) : x ∈ adjoin R ({x} : Set A) :=
   Algebra.subset_adjoin <| Set.mem_union_left _ (Set.mem_singleton x)
-#align star_subalgebra.self_mem_adjoin_singleton StarSubalgebra.self_mem_adjoin_singleton
+#align star_subalgebra.self_mem_adjoin_singleton StarAlgebra.self_mem_adjoin_singleton
 -/
 
-#print StarSubalgebra.star_self_mem_adjoin_singleton /-
+#print StarAlgebra.star_self_mem_adjoin_singleton /-
 theorem star_self_mem_adjoin_singleton (x : A) : star x ∈ adjoin R ({x} : Set A) :=
   star_mem <| self_mem_adjoin_singleton R x
-#align star_subalgebra.star_self_mem_adjoin_singleton StarSubalgebra.star_self_mem_adjoin_singleton
+#align star_subalgebra.star_self_mem_adjoin_singleton StarAlgebra.star_self_mem_adjoin_singleton
 -/
 
 variable {R}
 
-#print StarSubalgebra.gc /-
+#print StarAlgebra.gc /-
 protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A) coe :=
   by
   intro s S
@@ -591,30 +591,30 @@ protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A
   exact
     ⟨fun h => (Set.subset_union_left s _).trans h, fun h =>
       Set.union_subset h fun x hx => star_star x ▸ star_mem (show star x ∈ S from h hx)⟩
-#align star_subalgebra.gc StarSubalgebra.gc
+#align star_subalgebra.gc StarAlgebra.gc
 -/
 
-#print StarSubalgebra.gi /-
+#print StarAlgebra.gi /-
 /-- Galois insertion between `adjoin` and `coe`. -/
 protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) coe
     where
-  choice s hs := (adjoin R s).copy s <| le_antisymm (StarSubalgebra.gc.le_u_l s) hs
-  gc := StarSubalgebra.gc
-  le_l_u S := (StarSubalgebra.gc (S : Set A) (adjoin R S)).1 <| le_rfl
+  choice s hs := (adjoin R s).copy s <| le_antisymm (StarAlgebra.gc.le_u_l s) hs
+  gc := StarAlgebra.gc
+  le_l_u S := (StarAlgebra.gc (S : Set A) (adjoin R S)).1 <| le_rfl
   choice_eq _ _ := StarSubalgebra.copy_eq _ _ _
-#align star_subalgebra.gi StarSubalgebra.gi
+#align star_subalgebra.gi StarAlgebra.gi
 -/
 
-#print StarSubalgebra.adjoin_le /-
+#print StarAlgebra.adjoin_le /-
 theorem adjoin_le {S : StarSubalgebra R A} {s : Set A} (hs : s ⊆ S) : adjoin R s ≤ S :=
-  StarSubalgebra.gc.l_le hs
-#align star_subalgebra.adjoin_le StarSubalgebra.adjoin_le
+  StarAlgebra.gc.l_le hs
+#align star_subalgebra.adjoin_le StarAlgebra.adjoin_le
 -/
 
-#print StarSubalgebra.adjoin_le_iff /-
+#print StarAlgebra.adjoin_le_iff /-
 theorem adjoin_le_iff {S : StarSubalgebra R A} {s : Set A} : adjoin R s ≤ S ↔ s ⊆ S :=
-  StarSubalgebra.gc _ _
-#align star_subalgebra.adjoin_le_iff StarSubalgebra.adjoin_le_iff
+  StarAlgebra.gc _ _
+#align star_subalgebra.adjoin_le_iff StarAlgebra.adjoin_le_iff
 -/
 
 #print Subalgebra.starClosure_eq_adjoin /-
@@ -625,7 +625,7 @@ theorem Subalgebra.starClosure_eq_adjoin (S : Subalgebra R A) :
 #align subalgebra.star_closure_eq_adjoin Subalgebra.starClosure_eq_adjoin
 -/
 
-#print StarSubalgebra.adjoin_induction /-
+#print StarAlgebra.adjoin_induction /-
 /-- If some predicate holds for all `x ∈ (s : set A)` and this predicate is closed under the
 `algebra_map`, addition, multiplication and star operations, then it holds for `a ∈ adjoin R s`. -/
 theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin R s)
@@ -635,10 +635,10 @@ theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin
   Algebra.adjoin_induction h
     (fun x hx => hx.elim (fun hx => Hs x hx) fun hx => star_star x ▸ Hstar _ (Hs _ hx)) Halg Hadd
     Hmul
-#align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_induction
+#align star_subalgebra.adjoin_induction StarAlgebra.adjoin_induction
 -/
 
-#print StarSubalgebra.adjoin_induction₂ /-
+#print StarAlgebra.adjoin_induction₂ /-
 theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a ∈ adjoin R s)
     (hb : b ∈ adjoin R s) (Hs : ∀ x : A, x ∈ s → ∀ y : A, y ∈ s → p x y)
     (Halg : ∀ r₁ r₂ : R, p (algebraMap R A r₁) (algebraMap R A r₂))
@@ -660,10 +660,10 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
       star_star x ▸ star_star y ▸ Hstar _ _ (Hs _ hx _ hy)]
   · cases hx; exacts [Halg_left _ _ hx, star_star x ▸ Hstar_right _ _ (Halg_left r _ hx)]
   · cases hx; exacts [Halg_right _ _ hx, star_star x ▸ Hstar_left _ _ (Halg_right r _ hx)]
-#align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂
+#align star_subalgebra.adjoin_induction₂ StarAlgebra.adjoin_induction₂
 -/
 
-#print StarSubalgebra.adjoin_induction' /-
+#print StarAlgebra.adjoin_induction' /-
 /-- The difference with `star_subalgebra.adjoin_induction` is that this acts on the subtype. -/
 theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
     (Hs : ∀ (x) (h : x ∈ s), p ⟨x, subset_adjoin R s h⟩) (Halg : ∀ r, p (algebraMap R _ r))
@@ -679,12 +679,12 @@ theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
       fun x y hx hy =>
       Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨mul_mem hx' hy', Hmul _ _ hx hy⟩,
       fun x hx => Exists.elim hx fun hx' hx => ⟨star_mem hx', Hstar _ hx⟩]
-#align star_subalgebra.adjoin_induction' StarSubalgebra.adjoin_induction'
+#align star_subalgebra.adjoin_induction' StarAlgebra.adjoin_induction'
 -/
 
 variable (R)
 
-#print StarSubalgebra.adjoinCommSemiringOfComm /-
+#print StarAlgebra.adjoinCommSemiringOfComm /-
 /-- If all elements of `s : set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `star_subalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
 @[reducible]
@@ -706,10 +706,10 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
               star_star a ▸ (hcomm_star _ hb _ ha).symm, by
               simpa only [star_mul, star_star] using congr_arg star (hcomm _ hb _ ha)])
       exact congr_arg coe (mul_comm (⟨x, hx⟩ : Algebra.adjoin R (s ∪ star s)) ⟨y, hy⟩) }
-#align star_subalgebra.adjoin_comm_semiring_of_comm StarSubalgebra.adjoinCommSemiringOfComm
+#align star_subalgebra.adjoin_comm_semiring_of_comm StarAlgebra.adjoinCommSemiringOfComm
 -/
 
-#print StarSubalgebra.adjoinCommRingOfComm /-
+#print StarAlgebra.adjoinCommRingOfComm /-
 /-- If all elements of `s : set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `star_subalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
 @[reducible]
@@ -718,12 +718,11 @@ def adjoinCommRingOfComm (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ri
     (hcomm : ∀ a : A, a ∈ s → ∀ b : A, b ∈ s → a * b = b * a)
     (hcomm_star : ∀ a : A, a ∈ s → ∀ b : A, b ∈ s → a * star b = star b * a) :
     CommRing (adjoin R s) :=
-  { StarSubalgebra.adjoinCommSemiringOfComm R hcomm hcomm_star,
-    (adjoin R s).toSubalgebra.toRing with }
-#align star_subalgebra.adjoin_comm_ring_of_comm StarSubalgebra.adjoinCommRingOfComm
+  { StarAlgebra.adjoinCommSemiringOfComm R hcomm hcomm_star, (adjoin R s).toSubalgebra.toRing with }
+#align star_subalgebra.adjoin_comm_ring_of_comm StarAlgebra.adjoinCommRingOfComm
 -/
 
-#print StarSubalgebra.adjoinCommSemiringOfIsStarNormal /-
+#print StarAlgebra.adjoinCommSemiringOfIsStarNormal /-
 /-- The star subalgebra `star_subalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
 instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
@@ -731,17 +730,17 @@ instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
   adjoinCommSemiringOfComm R (fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb; rw [ha, hb])
     fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb;
     simpa only [ha, hb] using (star_comm_self' x).symm
-#align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormal
+#align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarAlgebra.adjoinCommSemiringOfIsStarNormal
 -/
 
-#print StarSubalgebra.adjoinCommRingOfIsStarNormal /-
+#print StarAlgebra.adjoinCommRingOfIsStarNormal /-
 /-- The star subalgebra `star_subalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
 instance adjoinCommRingOfIsStarNormal (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ring A]
     [Algebra R A] [StarRing A] [StarModule R A] (x : A) [IsStarNormal x] :
     CommRing (adjoin R ({x} : Set A)) :=
   { (adjoin R ({x} : Set A)).toSubalgebra.toRing with mul_comm := mul_comm }
-#align star_subalgebra.adjoin_comm_ring_of_is_star_normal StarSubalgebra.adjoinCommRingOfIsStarNormal
+#align star_subalgebra.adjoin_comm_ring_of_is_star_normal StarAlgebra.adjoinCommRingOfIsStarNormal
 -/
 
 /-! ### Complete lattice structure -/
@@ -750,7 +749,7 @@ instance adjoinCommRingOfIsStarNormal (R : Type u) {A : Type v} [CommRing R] [St
 variable {F R A B}
 
 instance : CompleteLattice (StarSubalgebra R A) :=
-  GaloisInsertion.liftCompleteLattice StarSubalgebra.gi
+  GaloisInsertion.liftCompleteLattice StarAlgebra.gi
 
 instance : Inhabited (StarSubalgebra R A) :=
   ⟨⊤⟩
@@ -948,8 +947,8 @@ theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (h
 #print StarAlgHom.map_adjoin /-
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
-  GaloisConnection.l_comm_of_u_comm Set.image_preimage (gc_map_comap f) StarSubalgebra.gc
-    StarSubalgebra.gc fun _ => rfl
+  GaloisConnection.l_comm_of_u_comm Set.image_preimage (gc_map_comap f) StarAlgebra.gc
+    StarAlgebra.gc fun _ => rfl
 #align star_alg_hom.map_adjoin StarAlgHom.map_adjoin
 -/
 

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

@@ -696,7 +696,7 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
       rintro ⟨x, hx⟩ ⟨y, hy⟩
       ext
       simp only [SetLike.coe_mk, MulMemClass.mk_mul_mk]
-      rw [← mem_to_subalgebra, adjoin_to_subalgebra] at hx hy 
+      rw [← mem_to_subalgebra, adjoin_to_subalgebra] at hx hy
       letI : CommSemiring (Algebra.adjoin R (s ∪ star s)) :=
         Algebra.adjoinCommSemiringOfComm R
           (by
@@ -728,8 +728,8 @@ def adjoinCommRingOfComm (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ri
 if `x` is normal. -/
 instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
     CommSemiring (adjoin R ({x} : Set A)) :=
-  adjoinCommSemiringOfComm R (fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb ; rw [ha, hb])
-    fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb ;
+  adjoinCommSemiringOfComm R (fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb; rw [ha, hb])
+    fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb;
     simpa only [ha, hb] using (star_comm_self' x).symm
 #align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormal
 -/
@@ -860,7 +860,7 @@ theorem coe_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i
 
 #print StarSubalgebra.mem_iInf /-
 theorem mem_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} {x : A} :
-    (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [iInf, mem_Inf, Set.forall_range_iff]
+    (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [iInf, mem_Inf, Set.forall_mem_range]
 #align star_subalgebra.mem_infi StarSubalgebra.mem_iInf
 -/
 

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

@@ -941,7 +941,7 @@ theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAl
 
 #print StarAlgHom.ext_of_adjoin_eq_top /-
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
-  FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
+  DFunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
 #align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_top
 -/
 
@@ -958,7 +958,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
   by
   refine'
-    FunLike.ext f g fun a =>
+    DFunLike.ext f g fun a =>
       adjoin_induction' a (fun x hx => _) (fun r => _) (fun x y hx hy => _) (fun x y hx hy => _)
         fun x hx => _
   · exact h ⟨x, subset_adjoin R s hx⟩ hx

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

@@ -3,11 +3,11 @@ Copyright (c) 2022 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Jireh Loreaux
 -/
-import Mathbin.Algebra.Star.StarAlgHom
-import Mathbin.Algebra.Algebra.Subalgebra.Basic
-import Mathbin.Algebra.Star.Pointwise
-import Mathbin.Algebra.Star.Module
-import Mathbin.RingTheory.Adjoin.Basic
+import Algebra.Star.StarAlgHom
+import Algebra.Algebra.Subalgebra.Basic
+import Algebra.Star.Pointwise
+import Algebra.Star.Module
+import RingTheory.Adjoin.Basic
 
 #align_import algebra.star.subalgebra from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
 

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

@@ -55,7 +55,7 @@ instance : StarMemClass (StarSubalgebra R A) A where star_mem s a := s.star_mem'
 instance : SubsemiringClass (StarSubalgebra R A) A
     where
   add_mem := add_mem'
-  mul_mem := mul_mem'
+  hMul_mem := hMul_mem'
   one_mem := one_mem'
   zero_mem := zero_mem'
 
@@ -68,7 +68,7 @@ instance (s : StarSubalgebra R A) : StarRing s
     where
   unit := star
   star_involutive r := Subtype.ext (star_star r)
-  star_mul r₁ r₂ := Subtype.ext (star_mul r₁ r₂)
+  star_hMul r₁ r₂ := Subtype.ext (star_hMul r₁ r₂)
   star_add r₁ r₂ := Subtype.ext (star_add r₁ r₂)
 
 instance (s : StarSubalgebra R A) : Algebra R s :=
@@ -132,7 +132,7 @@ protected def copy (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : StarSu
     where
   carrier := s
   add_mem' _ _ := hs.symm ▸ S.add_mem'
-  mul_mem' _ _ := hs.symm ▸ S.mul_mem'
+  hMul_mem' _ _ := hs.symm ▸ S.hMul_mem'
   algebraMap_mem' := hs.symm ▸ S.algebraMap_mem'
   star_mem' _ := hs.symm ▸ S.star_mem'
 #align star_subalgebra.copy StarSubalgebra.copy
@@ -178,7 +178,7 @@ theorem range_le : Set.range (algebraMap R A) ≤ S :=
 
 #print StarSubalgebra.smul_mem /-
 protected theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
-  (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem r) hx
+  (Algebra.smul_def r x).symm ▸ hMul_mem (S.algebraMap_mem r) hx
 #align star_subalgebra.smul_mem StarSubalgebra.smul_mem
 -/
 
@@ -429,7 +429,7 @@ instance : InvolutiveStar (Subalgebra R A)
     where
   unit S :=
     { carrier := star S.carrier
-      mul_mem' := fun x y hx hy =>
+      hMul_mem' := fun x y hx hy =>
         by
         simp only [Set.mem_star, Subalgebra.mem_carrier] at *
         exact (star_mul x y).symm ▸ mul_mem hy hx
@@ -798,7 +798,7 @@ theorem mem_sup_right {S T : StarSubalgebra R A} : ∀ {x : A}, x ∈ T → x 
 #print StarSubalgebra.mul_mem_sup /-
 theorem mul_mem_sup {S T : StarSubalgebra R A} {x y : A} (hx : x ∈ S) (hy : y ∈ T) :
     x * y ∈ S ⊔ T :=
-  mul_mem (mem_sup_left hx) (mem_sup_right hy)
+  hMul_mem (mem_sup_left hx) (mem_sup_right hy)
 #align star_subalgebra.mul_mem_sup StarSubalgebra.mul_mem_sup
 -/
 
@@ -917,7 +917,7 @@ variable [hF : StarAlgHomClass F R A B] (f g : F)
 def equalizer : StarSubalgebra R A
     where
   carrier := {a | f a = g a}
-  mul_mem' a b (ha : f a = g a) (hb : f b = g b) := by
+  hMul_mem' a b (ha : f a = g a) (hb : f b = g b) := by
     rw [Set.mem_setOf_eq, map_mul f, map_mul g, ha, hb]
   add_mem' a b (ha : f a = g a) (hb : f b = g b) := by
     rw [Set.mem_setOf_eq, map_add f, map_add g, ha, hb]

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Jireh Loreaux
-
-! This file was ported from Lean 3 source module algebra.star.subalgebra
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Star.StarAlgHom
 import Mathbin.Algebra.Algebra.Subalgebra.Basic
@@ -14,6 +9,8 @@ import Mathbin.Algebra.Star.Pointwise
 import Mathbin.Algebra.Star.Module
 import Mathbin.RingTheory.Adjoin.Basic
 
+#align_import algebra.star.subalgebra from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
 /-!
 # Star subalgebras
 

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

@@ -80,25 +80,33 @@ instance (s : StarSubalgebra R A) : Algebra R s :=
 instance (s : StarSubalgebra R A) : StarModule R s
     where star_smul r a := Subtype.ext (star_smul r a)
 
+#print StarSubalgebra.mem_carrier /-
 @[simp]
 theorem mem_carrier {s : StarSubalgebra R A} {x : A} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align star_subalgebra.mem_carrier StarSubalgebra.mem_carrier
+-/
 
+#print StarSubalgebra.ext /-
 @[ext]
 theorem ext {S T : StarSubalgebra R A} (h : ∀ x : A, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align star_subalgebra.ext StarSubalgebra.ext
+-/
 
+#print StarSubalgebra.mem_toSubalgebra /-
 @[simp]
 theorem mem_toSubalgebra {S : StarSubalgebra R A} {x} : x ∈ S.toSubalgebra ↔ x ∈ S :=
   Iff.rfl
 #align star_subalgebra.mem_to_subalgebra StarSubalgebra.mem_toSubalgebra
+-/
 
+#print StarSubalgebra.coe_toSubalgebra /-
 @[simp]
 theorem coe_toSubalgebra (S : StarSubalgebra R A) : (S.toSubalgebra : Set A) = S :=
   rfl
 #align star_subalgebra.coe_to_subalgebra StarSubalgebra.coe_toSubalgebra
+-/
 
 #print StarSubalgebra.toSubalgebra_injective /-
 theorem toSubalgebra_injective :
@@ -107,14 +115,18 @@ theorem toSubalgebra_injective :
 #align star_subalgebra.to_subalgebra_injective StarSubalgebra.toSubalgebra_injective
 -/
 
+#print StarSubalgebra.toSubalgebra_inj /-
 theorem toSubalgebra_inj {S U : StarSubalgebra R A} : S.toSubalgebra = U.toSubalgebra ↔ S = U :=
   toSubalgebra_injective.eq_iff
 #align star_subalgebra.to_subalgebra_inj StarSubalgebra.toSubalgebra_inj
+-/
 
+#print StarSubalgebra.toSubalgebra_le_iff /-
 theorem toSubalgebra_le_iff {S₁ S₂ : StarSubalgebra R A} :
     S₁.toSubalgebra ≤ S₂.toSubalgebra ↔ S₁ ≤ S₂ :=
   Iff.rfl
 #align star_subalgebra.to_subalgebra_le_iff StarSubalgebra.toSubalgebra_le_iff
+-/
 
 #print StarSubalgebra.copy /-
 /-- Copy of a star subalgebra with a new `carrier` equal to the old one. Useful to fix definitional
@@ -129,31 +141,43 @@ protected def copy (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : StarSu
 #align star_subalgebra.copy StarSubalgebra.copy
 -/
 
+#print StarSubalgebra.coe_copy /-
 @[simp]
 theorem coe_copy (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : (S.copy s hs : Set A) = s :=
   rfl
 #align star_subalgebra.coe_copy StarSubalgebra.coe_copy
+-/
 
+#print StarSubalgebra.copy_eq /-
 theorem copy_eq (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align star_subalgebra.copy_eq StarSubalgebra.copy_eq
+-/
 
 variable (S : StarSubalgebra R A)
 
+#print StarSubalgebra.algebraMap_mem /-
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
   S.algebraMap_mem' r
 #align star_subalgebra.algebra_map_mem StarSubalgebra.algebraMap_mem
+-/
 
+#print StarSubalgebra.rangeS_le /-
 theorem rangeS_le : (algebraMap R A).srange ≤ S.toSubalgebra.toSubsemiring := fun x ⟨r, hr⟩ =>
   hr ▸ S.algebraMap_mem r
 #align star_subalgebra.srange_le StarSubalgebra.rangeS_le
+-/
 
+#print StarSubalgebra.range_subset /-
 theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ => hr ▸ S.algebraMap_mem r
 #align star_subalgebra.range_subset StarSubalgebra.range_subset
+-/
 
+#print StarSubalgebra.range_le /-
 theorem range_le : Set.range (algebraMap R A) ≤ S :=
   S.range_subset
 #align star_subalgebra.range_le StarSubalgebra.range_le
+-/
 
 #print StarSubalgebra.smul_mem /-
 protected theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
@@ -167,20 +191,27 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 #align star_subalgebra.subtype StarSubalgebra.subtype
 -/
 
+#print StarSubalgebra.coe_subtype /-
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
   rfl
 #align star_subalgebra.coe_subtype StarSubalgebra.coe_subtype
+-/
 
+#print StarSubalgebra.subtype_apply /-
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
 #align star_subalgebra.subtype_apply StarSubalgebra.subtype_apply
+-/
 
+#print StarSubalgebra.toSubalgebra_subtype /-
 @[simp]
 theorem toSubalgebra_subtype : S.toSubalgebra.val = S.Subtype.toAlgHom :=
   rfl
 #align star_subalgebra.to_subalgebra_subtype StarSubalgebra.toSubalgebra_subtype
+-/
 
+#print StarSubalgebra.inclusion /-
 /-- The inclusion map between `star_subalgebra`s given by `subtype.map id` as a `star_alg_hom`. -/
 @[simps]
 def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆ₐ[R] S₂
@@ -193,17 +224,22 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
   commutes' z := rfl
   map_star' x := rfl
 #align star_subalgebra.inclusion StarSubalgebra.inclusion
+-/
 
+#print StarSubalgebra.inclusion_injective /-
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
   Set.inclusion_injective h
 #align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injective
+-/
 
+#print StarSubalgebra.subtype_comp_inclusion /-
 @[simp]
 theorem subtype_comp_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     S₂.Subtype.comp (inclusion h) = S₁.Subtype :=
   rfl
 #align star_subalgebra.subtype_comp_inclusion StarSubalgebra.subtype_comp_inclusion
+-/
 
 section Map
 
@@ -217,39 +253,53 @@ def map (f : A →⋆ₐ[R] B) (S : StarSubalgebra R A) : StarSubalgebra R B :=
 #align star_subalgebra.map StarSubalgebra.map
 -/
 
+#print StarSubalgebra.map_mono /-
 theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁ ≤ S₂ → S₁.map f ≤ S₂.map f :=
   Set.image_subset f
 #align star_subalgebra.map_mono StarSubalgebra.map_mono
+-/
 
+#print StarSubalgebra.map_injective /-
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
   ext <| Set.ext_iff.1 <| Set.image_injective.2 hf <| Set.ext <| SetLike.ext_iff.mp ih
 #align star_subalgebra.map_injective StarSubalgebra.map_injective
+-/
 
+#print StarSubalgebra.map_id /-
 @[simp]
 theorem map_id (S : StarSubalgebra R A) : S.map (StarAlgHom.id R A) = S :=
   SetLike.coe_injective <| Set.image_id _
 #align star_subalgebra.map_id StarSubalgebra.map_id
+-/
 
+#print StarSubalgebra.map_map /-
 theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ[R] B) :
     (S.map f).map g = S.map (g.comp f) :=
   SetLike.coe_injective <| Set.image_image _ _ _
 #align star_subalgebra.map_map StarSubalgebra.map_map
+-/
 
+#print StarSubalgebra.mem_map /-
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map
 #align star_subalgebra.mem_map StarSubalgebra.mem_map
+-/
 
+#print StarSubalgebra.map_toSubalgebra /-
 theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
     (S.map f).toSubalgebra = S.toSubalgebra.map f.toAlgHom :=
   SetLike.coe_injective rfl
 #align star_subalgebra.map_to_subalgebra StarSubalgebra.map_toSubalgebra
+-/
 
+#print StarSubalgebra.coe_map /-
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
   rfl
 #align star_subalgebra.coe_map StarSubalgebra.coe_map
+-/
 
 #print StarSubalgebra.comap /-
 /-- Preimage of a star subalgebra under an star algebra homomorphism. -/
@@ -259,20 +309,27 @@ def comap (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) : StarSubalgebra R A :
 #align star_subalgebra.comap StarSubalgebra.comap
 -/
 
+#print StarSubalgebra.map_le_iff_le_comap /-
 theorem map_le_iff_le_comap {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {U : StarSubalgebra R B} :
     map f S ≤ U ↔ S ≤ comap f U :=
   Set.image_subset_iff
 #align star_subalgebra.map_le_iff_le_comap StarSubalgebra.map_le_iff_le_comap
+-/
 
+#print StarSubalgebra.gc_map_comap /-
 theorem gc_map_comap (f : A →⋆ₐ[R] B) : GaloisConnection (map f) (comap f) := fun S U =>
   map_le_iff_le_comap
 #align star_subalgebra.gc_map_comap StarSubalgebra.gc_map_comap
+-/
 
+#print StarSubalgebra.comap_mono /-
 theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
     S₁ ≤ S₂ → S₁.comap f ≤ S₂.comap f :=
   Set.preimage_mono
 #align star_subalgebra.comap_mono StarSubalgebra.comap_mono
+-/
 
+#print StarSubalgebra.comap_injective /-
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
   ext fun b =>
@@ -280,27 +337,36 @@ theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     let this := SetLike.ext_iff.1 h x
     hx ▸ this
 #align star_subalgebra.comap_injective StarSubalgebra.comap_injective
+-/
 
+#print StarSubalgebra.comap_id /-
 @[simp]
 theorem comap_id (S : StarSubalgebra R A) : S.comap (StarAlgHom.id R A) = S :=
   SetLike.coe_injective <| Set.preimage_id
 #align star_subalgebra.comap_id StarSubalgebra.comap_id
+-/
 
+#print StarSubalgebra.comap_comap /-
 theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ[R] B) :
     (S.comap g).comap f = S.comap (g.comp f) :=
   SetLike.coe_injective <| Set.preimage_preimage
 #align star_subalgebra.comap_comap StarSubalgebra.comap_comap
+-/
 
+#print StarSubalgebra.mem_comap /-
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align star_subalgebra.mem_comap StarSubalgebra.mem_comap
+-/
 
+#print StarSubalgebra.coe_comap /-
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
     (S.comap f : Set A) = f ⁻¹' (S : Set B) :=
   rfl
 #align star_subalgebra.coe_comap StarSubalgebra.coe_comap
+-/
 
 end Map
 
@@ -308,10 +374,12 @@ section Centralizer
 
 variable (R) {A}
 
+#print Set.star_mem_centralizer /-
 theorem Set.star_mem_centralizer {a : A} {s : Set A} (h : ∀ a : A, a ∈ s → star a ∈ s)
     (ha : a ∈ Set.centralizer s) : star a ∈ Set.centralizer s := fun y hy => by
   simpa using congr_arg star (ha _ (h _ hy)).symm
 #align set.star_mem_centralizer Set.star_mem_centralizer
+-/
 
 #print StarSubalgebra.centralizer /-
 /-- The centralizer, or commutant, of a *-closed set as star subalgebra. -/
@@ -320,21 +388,27 @@ def centralizer (s : Set A) (w : ∀ a : A, a ∈ s → star a ∈ s) : StarSuba
 #align star_subalgebra.centralizer StarSubalgebra.centralizer
 -/
 
+#print StarSubalgebra.coe_centralizer /-
 @[simp]
 theorem coe_centralizer (s : Set A) (w : ∀ a : A, a ∈ s → star a ∈ s) :
     (centralizer R s w : Set A) = s.centralizer :=
   rfl
 #align star_subalgebra.coe_centralizer StarSubalgebra.coe_centralizer
+-/
 
+#print StarSubalgebra.mem_centralizer_iff /-
 theorem mem_centralizer_iff {s : Set A} {w} {z : A} :
     z ∈ centralizer R s w ↔ ∀ g ∈ s, g * z = z * g :=
   Iff.rfl
 #align star_subalgebra.mem_centralizer_iff StarSubalgebra.mem_centralizer_iff
+-/
 
+#print StarSubalgebra.centralizer_le /-
 theorem centralizer_le (s t : Set A) (ws : ∀ a : A, a ∈ s → star a ∈ s)
     (wt : ∀ a : A, a ∈ t → star a ∈ t) (h : s ⊆ t) : centralizer R t wt ≤ centralizer R s ws :=
   Set.centralizer_subset h
 #align star_subalgebra.centralizer_le StarSubalgebra.centralizer_le
+-/
 
 end Centralizer
 
@@ -375,20 +449,26 @@ instance : InvolutiveStar (Subalgebra R A)
     Subalgebra.ext fun x =>
       ⟨fun hx => star_star x ▸ hx, fun hx => ((star_star x).symm ▸ hx : star (star x) ∈ S)⟩
 
+#print Subalgebra.mem_star_iff /-
 @[simp]
 theorem mem_star_iff (S : Subalgebra R A) (x : A) : x ∈ star S ↔ star x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_star_iff Subalgebra.mem_star_iff
+-/
 
+#print Subalgebra.star_mem_star_iff /-
 @[simp]
 theorem star_mem_star_iff (S : Subalgebra R A) (x : A) : star x ∈ star S ↔ x ∈ S := by
   simpa only [star_star] using mem_star_iff S (star x)
 #align subalgebra.star_mem_star_iff Subalgebra.star_mem_star_iff
+-/
 
+#print Subalgebra.coe_star /-
 @[simp]
 theorem coe_star (S : Subalgebra R A) : ((star S : Subalgebra R A) : Set A) = star S :=
   rfl
 #align subalgebra.coe_star Subalgebra.coe_star
+-/
 
 #print Subalgebra.star_mono /-
 theorem star_mono : Monotone (star : Subalgebra R A → Subalgebra R A) := fun _ _ h _ hx => h hx
@@ -397,12 +477,14 @@ theorem star_mono : Monotone (star : Subalgebra R A → Subalgebra R A) := fun _
 
 variable (R)
 
+#print Subalgebra.star_adjoin_comm /-
 /-- The star operation on `subalgebra` commutes with `algebra.adjoin`. -/
 theorem star_adjoin_comm (s : Set A) : star (Algebra.adjoin R s) = Algebra.adjoin R (star s) :=
   have this : ∀ t : Set A, Algebra.adjoin R (star t) ≤ star (Algebra.adjoin R t) := fun t =>
     Algebra.adjoin_le fun x hx => Algebra.subset_adjoin hx
   le_antisymm (by simpa only [star_star] using Subalgebra.star_mono (this (star s))) (this s)
 #align subalgebra.star_adjoin_comm Subalgebra.star_adjoin_comm
+-/
 
 variable {R}
 
@@ -421,17 +503,21 @@ def starClosure (S : Subalgebra R A) : StarSubalgebra R A :=
 #align subalgebra.star_closure Subalgebra.starClosure
 -/
 
+#print Subalgebra.starClosure_le /-
 theorem starClosure_le {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂.toSubalgebra) :
     S₁.starClosure ≤ S₂ :=
   StarSubalgebra.toSubalgebra_le_iff.1 <|
     sup_le h fun x hx =>
       (star_star x ▸ star_mem (show star x ∈ S₂ from h <| (S₁.mem_star_iff _).1 hx) : x ∈ S₂)
 #align subalgebra.star_closure_le Subalgebra.starClosure_le
+-/
 
+#print Subalgebra.starClosure_le_iff /-
 theorem starClosure_le_iff {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} :
     S₁.starClosure ≤ S₂ ↔ S₁ ≤ S₂.toSubalgebra :=
   ⟨fun h => le_sup_left.trans h, starClosure_le⟩
 #align subalgebra.star_closure_le_iff Subalgebra.starClosure_le_iff
+-/
 
 end Subalgebra
 
@@ -500,6 +586,7 @@ theorem star_self_mem_adjoin_singleton (x : A) : star x ∈ adjoin R ({x} : Set
 
 variable {R}
 
+#print StarSubalgebra.gc /-
 protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A) coe :=
   by
   intro s S
@@ -508,7 +595,9 @@ protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A
     ⟨fun h => (Set.subset_union_left s _).trans h, fun h =>
       Set.union_subset h fun x hx => star_star x ▸ star_mem (show star x ∈ S from h hx)⟩
 #align star_subalgebra.gc StarSubalgebra.gc
+-/
 
+#print StarSubalgebra.gi /-
 /-- Galois insertion between `adjoin` and `coe`. -/
 protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) coe
     where
@@ -517,21 +606,29 @@ protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) coe
   le_l_u S := (StarSubalgebra.gc (S : Set A) (adjoin R S)).1 <| le_rfl
   choice_eq _ _ := StarSubalgebra.copy_eq _ _ _
 #align star_subalgebra.gi StarSubalgebra.gi
+-/
 
+#print StarSubalgebra.adjoin_le /-
 theorem adjoin_le {S : StarSubalgebra R A} {s : Set A} (hs : s ⊆ S) : adjoin R s ≤ S :=
   StarSubalgebra.gc.l_le hs
 #align star_subalgebra.adjoin_le StarSubalgebra.adjoin_le
+-/
 
+#print StarSubalgebra.adjoin_le_iff /-
 theorem adjoin_le_iff {S : StarSubalgebra R A} {s : Set A} : adjoin R s ≤ S ↔ s ⊆ S :=
   StarSubalgebra.gc _ _
 #align star_subalgebra.adjoin_le_iff StarSubalgebra.adjoin_le_iff
+-/
 
+#print Subalgebra.starClosure_eq_adjoin /-
 theorem Subalgebra.starClosure_eq_adjoin (S : Subalgebra R A) :
     S.starClosure = adjoin R (S : Set A) :=
   le_antisymm (Subalgebra.starClosure_le_iff.2 <| subset_adjoin R (S : Set A))
     (adjoin_le (le_sup_left : S ≤ S ⊔ star S))
 #align subalgebra.star_closure_eq_adjoin Subalgebra.starClosure_eq_adjoin
+-/
 
+#print StarSubalgebra.adjoin_induction /-
 /-- If some predicate holds for all `x ∈ (s : set A)` and this predicate is closed under the
 `algebra_map`, addition, multiplication and star operations, then it holds for `a ∈ adjoin R s`. -/
 theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin R s)
@@ -542,7 +639,9 @@ theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin
     (fun x hx => hx.elim (fun hx => Hs x hx) fun hx => star_star x ▸ Hstar _ (Hs _ hx)) Halg Hadd
     Hmul
 #align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_induction
+-/
 
+#print StarSubalgebra.adjoin_induction₂ /-
 theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a ∈ adjoin R s)
     (hb : b ∈ adjoin R s) (Hs : ∀ x : A, x ∈ s → ∀ y : A, y ∈ s → p x y)
     (Halg : ∀ r₁ r₂ : R, p (algebraMap R A r₁) (algebraMap R A r₂))
@@ -565,7 +664,9 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
   · cases hx; exacts [Halg_left _ _ hx, star_star x ▸ Hstar_right _ _ (Halg_left r _ hx)]
   · cases hx; exacts [Halg_right _ _ hx, star_star x ▸ Hstar_left _ _ (Halg_right r _ hx)]
 #align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂
+-/
 
+#print StarSubalgebra.adjoin_induction' /-
 /-- The difference with `star_subalgebra.adjoin_induction` is that this acts on the subtype. -/
 theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
     (Hs : ∀ (x) (h : x ∈ s), p ⟨x, subset_adjoin R s h⟩) (Halg : ∀ r, p (algebraMap R _ r))
@@ -582,9 +683,11 @@ theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
       Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨mul_mem hx' hy', Hmul _ _ hx hy⟩,
       fun x hx => Exists.elim hx fun hx' hx => ⟨star_mem hx', Hstar _ hx⟩]
 #align star_subalgebra.adjoin_induction' StarSubalgebra.adjoin_induction'
+-/
 
 variable (R)
 
+#print StarSubalgebra.adjoinCommSemiringOfComm /-
 /-- If all elements of `s : set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `star_subalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
 @[reducible]
@@ -607,7 +710,9 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
               simpa only [star_mul, star_star] using congr_arg star (hcomm _ hb _ ha)])
       exact congr_arg coe (mul_comm (⟨x, hx⟩ : Algebra.adjoin R (s ∪ star s)) ⟨y, hy⟩) }
 #align star_subalgebra.adjoin_comm_semiring_of_comm StarSubalgebra.adjoinCommSemiringOfComm
+-/
 
+#print StarSubalgebra.adjoinCommRingOfComm /-
 /-- If all elements of `s : set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `star_subalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
 @[reducible]
@@ -619,7 +724,9 @@ def adjoinCommRingOfComm (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ri
   { StarSubalgebra.adjoinCommSemiringOfComm R hcomm hcomm_star,
     (adjoin R s).toSubalgebra.toRing with }
 #align star_subalgebra.adjoin_comm_ring_of_comm StarSubalgebra.adjoinCommRingOfComm
+-/
 
+#print StarSubalgebra.adjoinCommSemiringOfIsStarNormal /-
 /-- The star subalgebra `star_subalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
 instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
@@ -628,7 +735,9 @@ instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
     fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb ;
     simpa only [ha, hb] using (star_comm_self' x).symm
 #align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormal
+-/
 
+#print StarSubalgebra.adjoinCommRingOfIsStarNormal /-
 /-- The star subalgebra `star_subalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
 instance adjoinCommRingOfIsStarNormal (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ring A]
@@ -636,6 +745,7 @@ instance adjoinCommRingOfIsStarNormal (R : Type u) {A : Type v} [CommRing R] [St
     CommRing (adjoin R ({x} : Set A)) :=
   { (adjoin R ({x} : Set A)).toSubalgebra.toRing with mul_comm := mul_comm }
 #align star_subalgebra.adjoin_comm_ring_of_is_star_normal StarSubalgebra.adjoinCommRingOfIsStarNormal
+-/
 
 /-! ### Complete lattice structure -/
 
@@ -648,106 +758,148 @@ instance : CompleteLattice (StarSubalgebra R A) :=
 instance : Inhabited (StarSubalgebra R A) :=
   ⟨⊤⟩
 
+#print StarSubalgebra.coe_top /-
 @[simp]
 theorem coe_top : (↑(⊤ : StarSubalgebra R A) : Set A) = Set.univ :=
   rfl
 #align star_subalgebra.coe_top StarSubalgebra.coe_top
+-/
 
+#print StarSubalgebra.mem_top /-
 @[simp]
 theorem mem_top {x : A} : x ∈ (⊤ : StarSubalgebra R A) :=
   Set.mem_univ x
 #align star_subalgebra.mem_top StarSubalgebra.mem_top
+-/
 
+#print StarSubalgebra.top_toSubalgebra /-
 @[simp]
 theorem top_toSubalgebra : (⊤ : StarSubalgebra R A).toSubalgebra = ⊤ :=
   rfl
 #align star_subalgebra.top_to_subalgebra StarSubalgebra.top_toSubalgebra
+-/
 
+#print StarSubalgebra.toSubalgebra_eq_top /-
 @[simp]
 theorem toSubalgebra_eq_top {S : StarSubalgebra R A} : S.toSubalgebra = ⊤ ↔ S = ⊤ :=
   StarSubalgebra.toSubalgebra_injective.eq_iff' top_toSubalgebra
 #align star_subalgebra.to_subalgebra_eq_top StarSubalgebra.toSubalgebra_eq_top
+-/
 
+#print StarSubalgebra.mem_sup_left /-
 theorem mem_sup_left {S T : StarSubalgebra R A} : ∀ {x : A}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
 #align star_subalgebra.mem_sup_left StarSubalgebra.mem_sup_left
+-/
 
+#print StarSubalgebra.mem_sup_right /-
 theorem mem_sup_right {S T : StarSubalgebra R A} : ∀ {x : A}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
 #align star_subalgebra.mem_sup_right StarSubalgebra.mem_sup_right
+-/
 
+#print StarSubalgebra.mul_mem_sup /-
 theorem mul_mem_sup {S T : StarSubalgebra R A} {x y : A} (hx : x ∈ S) (hy : y ∈ T) :
     x * y ∈ S ⊔ T :=
   mul_mem (mem_sup_left hx) (mem_sup_right hy)
 #align star_subalgebra.mul_mem_sup StarSubalgebra.mul_mem_sup
+-/
 
+#print StarSubalgebra.map_sup /-
 theorem map_sup (f : A →⋆ₐ[R] B) (S T : StarSubalgebra R A) : map f (S ⊔ T) = map f S ⊔ map f T :=
   (StarSubalgebra.gc_map_comap f).l_sup
 #align star_subalgebra.map_sup StarSubalgebra.map_sup
+-/
 
+#print StarSubalgebra.coe_inf /-
 @[simp, norm_cast]
 theorem coe_inf (S T : StarSubalgebra R A) : (↑(S ⊓ T) : Set A) = S ∩ T :=
   rfl
 #align star_subalgebra.coe_inf StarSubalgebra.coe_inf
+-/
 
+#print StarSubalgebra.mem_inf /-
 @[simp]
 theorem mem_inf {S T : StarSubalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x ∈ T :=
   Iff.rfl
 #align star_subalgebra.mem_inf StarSubalgebra.mem_inf
+-/
 
+#print StarSubalgebra.inf_toSubalgebra /-
 @[simp]
 theorem inf_toSubalgebra (S T : StarSubalgebra R A) :
     (S ⊓ T).toSubalgebra = S.toSubalgebra ⊓ T.toSubalgebra :=
   rfl
 #align star_subalgebra.inf_to_subalgebra StarSubalgebra.inf_toSubalgebra
+-/
 
+#print StarSubalgebra.coe_sInf /-
 @[simp, norm_cast]
 theorem coe_sInf (S : Set (StarSubalgebra R A)) : (↑(sInf S) : Set A) = ⋂ s ∈ S, ↑s :=
   sInf_image
 #align star_subalgebra.coe_Inf StarSubalgebra.coe_sInf
+-/
 
+#print StarSubalgebra.mem_sInf /-
 theorem mem_sInf {S : Set (StarSubalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p := by
   simp only [← SetLike.mem_coe, coe_Inf, Set.mem_iInter₂]
 #align star_subalgebra.mem_Inf StarSubalgebra.mem_sInf
+-/
 
+#print StarSubalgebra.sInf_toSubalgebra /-
 @[simp]
 theorem sInf_toSubalgebra (S : Set (StarSubalgebra R A)) :
     (sInf S).toSubalgebra = sInf (StarSubalgebra.toSubalgebra '' S) :=
   SetLike.coe_injective <| by simp
 #align star_subalgebra.Inf_to_subalgebra StarSubalgebra.sInf_toSubalgebra
+-/
 
+#print StarSubalgebra.coe_iInf /-
 @[simp, norm_cast]
 theorem coe_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
   simp [iInf]
 #align star_subalgebra.coe_infi StarSubalgebra.coe_iInf
+-/
 
+#print StarSubalgebra.mem_iInf /-
 theorem mem_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} {x : A} :
     (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [iInf, mem_Inf, Set.forall_range_iff]
 #align star_subalgebra.mem_infi StarSubalgebra.mem_iInf
+-/
 
+#print StarSubalgebra.iInf_toSubalgebra /-
 @[simp]
 theorem iInf_toSubalgebra {ι : Sort _} (S : ι → StarSubalgebra R A) :
     (⨅ i, S i).toSubalgebra = ⨅ i, (S i).toSubalgebra :=
   SetLike.coe_injective <| by simp
 #align star_subalgebra.infi_to_subalgebra StarSubalgebra.iInf_toSubalgebra
+-/
 
+#print StarSubalgebra.bot_toSubalgebra /-
 theorem bot_toSubalgebra : (⊥ : StarSubalgebra R A).toSubalgebra = ⊥ := by
   change Algebra.adjoin R (∅ ∪ star ∅) = Algebra.adjoin R ∅; simp
 #align star_subalgebra.bot_to_subalgebra StarSubalgebra.bot_toSubalgebra
+-/
 
+#print StarSubalgebra.mem_bot /-
 theorem mem_bot {x : A} : x ∈ (⊥ : StarSubalgebra R A) ↔ x ∈ Set.range (algebraMap R A) := by
   rw [← mem_to_subalgebra, bot_to_subalgebra, Algebra.mem_bot]
 #align star_subalgebra.mem_bot StarSubalgebra.mem_bot
+-/
 
+#print StarSubalgebra.coe_bot /-
 @[simp]
 theorem coe_bot : ((⊥ : StarSubalgebra R A) : Set A) = Set.range (algebraMap R A) := by
   simp [Set.ext_iff, mem_bot]
 #align star_subalgebra.coe_bot StarSubalgebra.coe_bot
+-/
 
+#print StarSubalgebra.eq_top_iff /-
 theorem eq_top_iff {S : StarSubalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=
   ⟨fun h x => by rw [h] <;> exact mem_top, fun h => by
     ext x <;> exact ⟨fun _ => mem_top, fun _ => h x⟩⟩
 #align star_subalgebra.eq_top_iff StarSubalgebra.eq_top_iff
+-/
 
 end StarSubalgebra
 
@@ -763,8 +915,6 @@ variable [Semiring B] [Algebra R B] [StarRing B]
 
 variable [hF : StarAlgHomClass F R A B] (f g : F)
 
-include hF
-
 #print StarAlgHom.equalizer /-
 /-- The equalizer of two star `R`-algebra homomorphisms. -/
 def equalizer : StarSubalgebra R A
@@ -779,27 +929,34 @@ def equalizer : StarSubalgebra R A
 #align star_alg_hom.equalizer StarAlgHom.equalizer
 -/
 
+#print StarAlgHom.mem_equalizer /-
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
   Iff.rfl
 #align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizer
+-/
 
+#print StarAlgHom.adjoin_le_equalizer /-
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
 #align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizer
+-/
 
+#print StarAlgHom.ext_of_adjoin_eq_top /-
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
 #align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_top
+-/
 
-omit hF
-
+#print StarAlgHom.map_adjoin /-
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
   GaloisConnection.l_comm_of_u_comm Set.image_preimage (gc_map_comap f) StarSubalgebra.gc
     StarSubalgebra.gc fun _ => rfl
 #align star_alg_hom.map_adjoin StarAlgHom.map_adjoin
+-/
 
+#print StarAlgHom.ext_adjoin /-
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
   by
@@ -813,7 +970,9 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
   · rw [map_mul, map_mul, hx, hy]
   · rw [map_star, map_star, hx]
 #align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoin
+-/
 
+#print StarAlgHom.ext_adjoin_singleton /-
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=
   ext_adjoin fun x hx =>
@@ -821,6 +980,7 @@ theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A
           Subtype.ext <| Set.mem_singleton_iff.mp hx).symm ▸
       h
 #align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singleton
+-/
 
 end StarAlgHom
 

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

@@ -769,7 +769,7 @@ include hF
 /-- The equalizer of two star `R`-algebra homomorphisms. -/
 def equalizer : StarSubalgebra R A
     where
-  carrier := { a | f a = g a }
+  carrier := {a | f a = g a}
   mul_mem' a b (ha : f a = g a) (hb : f b = g b) := by
     rw [Set.mem_setOf_eq, map_mul f, map_mul g, ha, hb]
   add_mem' a b (ha : f a = g a) (hb : f b = g b) := by

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

@@ -31,7 +31,7 @@ universe u v
 #print StarSubalgebra /-
 /-- A *-subalgebra is a subalgebra of a *-algebra which is closed under *. -/
 structure StarSubalgebra (R : Type u) (A : Type v) [CommSemiring R] [StarRing R] [Semiring A]
-  [StarRing A] [Algebra R A] [StarModule R A] extends Subalgebra R A : Type v where
+    [StarRing A] [Algebra R A] [StarModule R A] extends Subalgebra R A : Type v where
   star_mem' {a} : a ∈ carrier → star a ∈ carrier
 #align star_subalgebra StarSubalgebra
 -/
@@ -51,7 +51,7 @@ variable [Semiring B] [StarRing B] [Algebra R B] [StarModule R B]
 variable [Semiring C] [StarRing C] [Algebra R C] [StarModule R C]
 
 instance : SetLike (StarSubalgebra R A) A :=
-  ⟨StarSubalgebra.carrier, fun p q h => by cases p <;> cases q <;> congr ⟩
+  ⟨StarSubalgebra.carrier, fun p q h => by cases p <;> cases q <;> congr⟩
 
 instance : StarMemClass (StarSubalgebra R A) A where star_mem s a := s.star_mem'
 
@@ -559,11 +559,11 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
     Algebra.adjoin_induction₂ ha hb (fun x hx y hy => _) Halg (fun r x hx => _) (fun r x hx => _)
       Hadd_left Hadd_right Hmul_left Hmul_right
   · cases hx <;> cases hy
-    exacts[Hs x hx y hy, star_star y ▸ Hstar_right _ _ (Hs _ hx _ hy),
+    exacts [Hs x hx y hy, star_star y ▸ Hstar_right _ _ (Hs _ hx _ hy),
       star_star x ▸ Hstar_left _ _ (Hs _ hx _ hy),
       star_star x ▸ star_star y ▸ Hstar _ _ (Hs _ hx _ hy)]
-  · cases hx; exacts[Halg_left _ _ hx, star_star x ▸ Hstar_right _ _ (Halg_left r _ hx)]
-  · cases hx; exacts[Halg_right _ _ hx, star_star x ▸ Hstar_left _ _ (Halg_right r _ hx)]
+  · cases hx; exacts [Halg_left _ _ hx, star_star x ▸ Hstar_right _ _ (Halg_left r _ hx)]
+  · cases hx; exacts [Halg_right _ _ hx, star_star x ▸ Hstar_left _ _ (Halg_right r _ hx)]
 #align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂
 
 /-- The difference with `star_subalgebra.adjoin_induction` is that this acts on the subtype. -/
@@ -575,7 +575,7 @@ theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
     by
     refine' Exists.elim _ fun (hb : b ∈ adjoin R s) (hc : p ⟨b, hb⟩) => hc
     apply adjoin_induction hb
-    exacts[fun x hx => ⟨subset_adjoin R s hx, Hs x hx⟩, fun r =>
+    exacts [fun x hx => ⟨subset_adjoin R s hx, Hs x hx⟩, fun r =>
       ⟨StarSubalgebra.algebraMap_mem _ r, Halg r⟩, fun x y hx hy =>
       Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨add_mem hx' hy', Hadd _ _ hx hy⟩,
       fun x y hx hy =>
@@ -596,13 +596,13 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
       rintro ⟨x, hx⟩ ⟨y, hy⟩
       ext
       simp only [SetLike.coe_mk, MulMemClass.mk_mul_mk]
-      rw [← mem_to_subalgebra, adjoin_to_subalgebra] at hx hy
+      rw [← mem_to_subalgebra, adjoin_to_subalgebra] at hx hy 
       letI : CommSemiring (Algebra.adjoin R (s ∪ star s)) :=
         Algebra.adjoinCommSemiringOfComm R
           (by
             intro a ha b hb
             cases ha <;> cases hb
-            exacts[hcomm _ ha _ hb, star_star b ▸ hcomm_star _ ha _ hb,
+            exacts [hcomm _ ha _ hb, star_star b ▸ hcomm_star _ ha _ hb,
               star_star a ▸ (hcomm_star _ hb _ ha).symm, by
               simpa only [star_mul, star_star] using congr_arg star (hcomm _ hb _ ha)])
       exact congr_arg coe (mul_comm (⟨x, hx⟩ : Algebra.adjoin R (s ∪ star s)) ⟨y, hy⟩) }
@@ -624,8 +624,8 @@ def adjoinCommRingOfComm (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ri
 if `x` is normal. -/
 instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
     CommSemiring (adjoin R ({x} : Set A)) :=
-  adjoinCommSemiringOfComm R (fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb; rw [ha, hb])
-    fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb;
+  adjoinCommSemiringOfComm R (fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb ; rw [ha, hb])
+    fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb ;
     simpa only [ha, hb] using (star_comm_self' x).symm
 #align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormal
 

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

@@ -595,7 +595,7 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
     mul_comm := by
       rintro ⟨x, hx⟩ ⟨y, hy⟩
       ext
-      simp only [[anonymous], MulMemClass.mk_mul_mk]
+      simp only [SetLike.coe_mk, MulMemClass.mk_mul_mk]
       rw [← mem_to_subalgebra, adjoin_to_subalgebra] at hx hy
       letI : CommSemiring (Algebra.adjoin R (s ∪ star s)) :=
         Algebra.adjoinCommSemiringOfComm R

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

@@ -345,7 +345,7 @@ end StarSubalgebra
 
 namespace Subalgebra
 
-open Pointwise
+open scoped Pointwise
 
 variable {F R A B : Type _} [CommSemiring R] [StarRing R]
 

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

@@ -80,45 +80,21 @@ instance (s : StarSubalgebra R A) : Algebra R s :=
 instance (s : StarSubalgebra R A) : StarModule R s
     where star_smul r a := Subtype.ext (star_smul r a)
 
-/- warning: star_subalgebra.mem_carrier -> StarSubalgebra.mem_carrier 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {x : A}, Iff (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (StarSubalgebra.carrier.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {s : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {x : A}, Iff (Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3) (Subalgebra.toSubsemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)))))) (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x s)
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_carrier StarSubalgebra.mem_carrierₓ'. -/
 @[simp]
 theorem mem_carrier {s : StarSubalgebra R A} {x : A} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align star_subalgebra.mem_carrier StarSubalgebra.mem_carrier
 
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 @[ext]
 theorem ext {S T : StarSubalgebra R A} (h : ∀ x : A, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align star_subalgebra.ext StarSubalgebra.ext
 
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 @[simp]
 theorem mem_toSubalgebra {S : StarSubalgebra R A} {x} : x ∈ S.toSubalgebra ↔ x ∈ S :=
   Iff.rfl
 #align star_subalgebra.mem_to_subalgebra StarSubalgebra.mem_toSubalgebra
 
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 @[simp]
 theorem coe_toSubalgebra (S : StarSubalgebra R A) : (S.toSubalgebra : Set A) = S :=
   rfl
@@ -131,22 +107,10 @@ theorem toSubalgebra_injective :
 #align star_subalgebra.to_subalgebra_injective StarSubalgebra.toSubalgebra_injective
 -/
 
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 theorem toSubalgebra_inj {S U : StarSubalgebra R A} : S.toSubalgebra = U.toSubalgebra ↔ S = U :=
   toSubalgebra_injective.eq_iff
 #align star_subalgebra.to_subalgebra_inj StarSubalgebra.toSubalgebra_inj
 
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 theorem toSubalgebra_le_iff {S₁ S₂ : StarSubalgebra R A} :
     S₁.toSubalgebra ≤ S₂.toSubalgebra ↔ S₁ ≤ S₂ :=
   Iff.rfl
@@ -165,64 +129,28 @@ protected def copy (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : StarSu
 #align star_subalgebra.copy StarSubalgebra.copy
 -/
 
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 @[simp]
 theorem coe_copy (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : (S.copy s hs : Set A) = s :=
   rfl
 #align star_subalgebra.coe_copy StarSubalgebra.coe_copy
 
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 theorem copy_eq (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align star_subalgebra.copy_eq StarSubalgebra.copy_eq
 
 variable (S : StarSubalgebra R A)
 
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 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
   S.algebraMap_mem' r
 #align star_subalgebra.algebra_map_mem StarSubalgebra.algebraMap_mem
 
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 theorem rangeS_le : (algebraMap R A).srange ≤ S.toSubalgebra.toSubsemiring := fun x ⟨r, hr⟩ =>
   hr ▸ S.algebraMap_mem r
 #align star_subalgebra.srange_le StarSubalgebra.rangeS_le
 
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 theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ => hr ▸ S.algebraMap_mem r
 #align star_subalgebra.range_subset StarSubalgebra.range_subset
 
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 theorem range_le : Set.range (algebraMap R A) ≤ S :=
   S.range_subset
 #align star_subalgebra.range_le StarSubalgebra.range_le
@@ -239,32 +167,20 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 #align star_subalgebra.subtype StarSubalgebra.subtype
 -/
 
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 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
   rfl
 #align star_subalgebra.coe_subtype StarSubalgebra.coe_subtype
 
-/- warning: star_subalgebra.subtype_apply -> StarSubalgebra.subtype_apply is a dubious translation:
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 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
 #align star_subalgebra.subtype_apply StarSubalgebra.subtype_apply
 
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 @[simp]
 theorem toSubalgebra_subtype : S.toSubalgebra.val = S.Subtype.toAlgHom :=
   rfl
 #align star_subalgebra.to_subalgebra_subtype StarSubalgebra.toSubalgebra_subtype
 
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 /-- The inclusion map between `star_subalgebra`s given by `subtype.map id` as a `star_alg_hom`. -/
 @[simps]
 def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆ₐ[R] S₂
@@ -278,17 +194,11 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
   map_star' x := rfl
 #align star_subalgebra.inclusion StarSubalgebra.inclusion
 
-/- warning: star_subalgebra.inclusion_injective -> StarSubalgebra.inclusion_injective is a dubious translation:
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 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
   Set.inclusion_injective h
 #align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injective
 
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 @[simp]
 theorem subtype_comp_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     S₂.Subtype.comp (inclusion h) = S₁.Subtype :=
@@ -307,59 +217,35 @@ def map (f : A →⋆ₐ[R] B) (S : StarSubalgebra R A) : StarSubalgebra R B :=
 #align star_subalgebra.map StarSubalgebra.map
 -/
 
-/- warning: star_subalgebra.map_mono -> StarSubalgebra.map_mono is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_mono StarSubalgebra.map_monoₓ'. -/
 theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁ ≤ S₂ → S₁.map f ≤ S₂.map f :=
   Set.image_subset f
 #align star_subalgebra.map_mono StarSubalgebra.map_mono
 
-/- warning: star_subalgebra.map_injective -> StarSubalgebra.map_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
   ext <| Set.ext_iff.1 <| Set.image_injective.2 hf <| Set.ext <| SetLike.ext_iff.mp ih
 #align star_subalgebra.map_injective StarSubalgebra.map_injective
 
-/- warning: star_subalgebra.map_id -> StarSubalgebra.map_id is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_id StarSubalgebra.map_idₓ'. -/
 @[simp]
 theorem map_id (S : StarSubalgebra R A) : S.map (StarAlgHom.id R A) = S :=
   SetLike.coe_injective <| Set.image_id _
 #align star_subalgebra.map_id StarSubalgebra.map_id
 
-/- warning: star_subalgebra.map_map -> StarSubalgebra.map_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_map StarSubalgebra.map_mapₓ'. -/
 theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ[R] B) :
     (S.map f).map g = S.map (g.comp f) :=
   SetLike.coe_injective <| Set.image_image _ _ _
 #align star_subalgebra.map_map StarSubalgebra.map_map
 
-/- warning: star_subalgebra.mem_map -> StarSubalgebra.mem_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map
 #align star_subalgebra.mem_map StarSubalgebra.mem_map
 
-/- warning: star_subalgebra.map_to_subalgebra -> StarSubalgebra.map_toSubalgebra is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_to_subalgebra StarSubalgebra.map_toSubalgebraₓ'. -/
 theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
     (S.map f).toSubalgebra = S.toSubalgebra.map f.toAlgHom :=
   SetLike.coe_injective rfl
 #align star_subalgebra.map_to_subalgebra StarSubalgebra.map_toSubalgebra
 
-/- warning: star_subalgebra.coe_map -> StarSubalgebra.coe_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
   rfl
@@ -373,32 +259,20 @@ def comap (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) : StarSubalgebra R A :
 #align star_subalgebra.comap StarSubalgebra.comap
 -/
 
-/- warning: star_subalgebra.map_le_iff_le_comap -> StarSubalgebra.map_le_iff_le_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_le_iff_le_comap StarSubalgebra.map_le_iff_le_comapₓ'. -/
 theorem map_le_iff_le_comap {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {U : StarSubalgebra R B} :
     map f S ≤ U ↔ S ≤ comap f U :=
   Set.image_subset_iff
 #align star_subalgebra.map_le_iff_le_comap StarSubalgebra.map_le_iff_le_comap
 
-/- warning: star_subalgebra.gc_map_comap -> StarSubalgebra.gc_map_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.gc_map_comap StarSubalgebra.gc_map_comapₓ'. -/
 theorem gc_map_comap (f : A →⋆ₐ[R] B) : GaloisConnection (map f) (comap f) := fun S U =>
   map_le_iff_le_comap
 #align star_subalgebra.gc_map_comap StarSubalgebra.gc_map_comap
 
-/- warning: star_subalgebra.comap_mono -> StarSubalgebra.comap_mono is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_mono StarSubalgebra.comap_monoₓ'. -/
 theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
     S₁ ≤ S₂ → S₁.comap f ≤ S₂.comap f :=
   Set.preimage_mono
 #align star_subalgebra.comap_mono StarSubalgebra.comap_mono
 
-/- warning: star_subalgebra.comap_injective -> StarSubalgebra.comap_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
   ext fun b =>
@@ -407,36 +281,21 @@ theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     hx ▸ this
 #align star_subalgebra.comap_injective StarSubalgebra.comap_injective
 
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 @[simp]
 theorem comap_id (S : StarSubalgebra R A) : S.comap (StarAlgHom.id R A) = S :=
   SetLike.coe_injective <| Set.preimage_id
 #align star_subalgebra.comap_id StarSubalgebra.comap_id
 
-/- warning: star_subalgebra.comap_comap -> StarSubalgebra.comap_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_comap StarSubalgebra.comap_comapₓ'. -/
 theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ[R] B) :
     (S.comap g).comap f = S.comap (g.comp f) :=
   SetLike.coe_injective <| Set.preimage_preimage
 #align star_subalgebra.comap_comap StarSubalgebra.comap_comap
 
-/- warning: star_subalgebra.mem_comap -> StarSubalgebra.mem_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align star_subalgebra.mem_comap StarSubalgebra.mem_comap
 
-/- warning: star_subalgebra.coe_comap -> StarSubalgebra.coe_comap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
     (S.comap f : Set A) = f ⁻¹' (S : Set B) :=
@@ -449,12 +308,6 @@ section Centralizer
 
 variable (R) {A}
 
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-Case conversion may be inaccurate. Consider using '#align set.star_mem_centralizer Set.star_mem_centralizerₓ'. -/
 theorem Set.star_mem_centralizer {a : A} {s : Set A} (h : ∀ a : A, a ∈ s → star a ∈ s)
     (ha : a ∈ Set.centralizer s) : star a ∈ Set.centralizer s := fun y hy => by
   simpa using congr_arg star (ha _ (h _ hy)).symm
@@ -467,35 +320,17 @@ def centralizer (s : Set A) (w : ∀ a : A, a ∈ s → star a ∈ s) : StarSuba
 #align star_subalgebra.centralizer StarSubalgebra.centralizer
 -/
 
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 @[simp]
 theorem coe_centralizer (s : Set A) (w : ∀ a : A, a ∈ s → star a ∈ s) :
     (centralizer R s w : Set A) = s.centralizer :=
   rfl
 #align star_subalgebra.coe_centralizer StarSubalgebra.coe_centralizer
 
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_centralizer_iff StarSubalgebra.mem_centralizer_iffₓ'. -/
 theorem mem_centralizer_iff {s : Set A} {w} {z : A} :
     z ∈ centralizer R s w ↔ ∀ g ∈ s, g * z = z * g :=
   Iff.rfl
 #align star_subalgebra.mem_centralizer_iff StarSubalgebra.mem_centralizer_iff
 
-/- warning: star_subalgebra.centralizer_le -> StarSubalgebra.centralizer_le 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (s : Set.{u2} A) (t : Set.{u2} A) (ws : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)) (wt : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a t) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) t)), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s t) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 t wt) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s ws))
-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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (s : Set.{u2} A) (t : Set.{u2} A) (ws : forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)) (wt : forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a t) -> (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) t)), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) s t) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 t wt) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s ws))
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.centralizer_le StarSubalgebra.centralizer_leₓ'. -/
 theorem centralizer_le (s t : Set A) (ws : ∀ a : A, a ∈ s → star a ∈ s)
     (wt : ∀ a : A, a ∈ t → star a ∈ t) (h : s ⊆ t) : centralizer R t wt ≤ centralizer R s ws :=
   Set.centralizer_subset h
@@ -540,34 +375,16 @@ instance : InvolutiveStar (Subalgebra R A)
     Subalgebra.ext fun x =>
       ⟨fun hx => star_star x ▸ hx, fun hx => ((star_star x).symm ▸ hx : star (star x) ∈ S)⟩
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align subalgebra.mem_star_iff Subalgebra.mem_star_iffₓ'. -/
 @[simp]
 theorem mem_star_iff (S : Subalgebra R A) (x : A) : x ∈ star S ↔ star x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_star_iff Subalgebra.mem_star_iff
 
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 @[simp]
 theorem star_mem_star_iff (S : Subalgebra R A) (x : A) : star x ∈ star S ↔ x ∈ S := by
   simpa only [star_star] using mem_star_iff S (star x)
 #align subalgebra.star_mem_star_iff Subalgebra.star_mem_star_iff
 
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 @[simp]
 theorem coe_star (S : Subalgebra R A) : ((star S : Subalgebra R A) : Set A) = star S :=
   rfl
@@ -580,12 +397,6 @@ theorem star_mono : Monotone (star : Subalgebra R A → Subalgebra R A) := fun _
 
 variable (R)
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.star_adjoin_comm Subalgebra.star_adjoin_commₓ'. -/
 /-- The star operation on `subalgebra` commutes with `algebra.adjoin`. -/
 theorem star_adjoin_comm (s : Set A) : star (Algebra.adjoin R s) = Algebra.adjoin R (star s) :=
   have this : ∀ t : Set A, Algebra.adjoin R (star t) ≤ star (Algebra.adjoin R t) := fun t =>
@@ -610,12 +421,6 @@ def starClosure (S : Subalgebra R A) : StarSubalgebra R A :=
 #align subalgebra.star_closure Subalgebra.starClosure
 -/
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.star_closure_le Subalgebra.starClosure_leₓ'. -/
 theorem starClosure_le {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂.toSubalgebra) :
     S₁.starClosure ≤ S₂ :=
   StarSubalgebra.toSubalgebra_le_iff.1 <|
@@ -623,12 +428,6 @@ theorem starClosure_le {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} (h :
       (star_star x ▸ star_mem (show star x ∈ S₂ from h <| (S₁.mem_star_iff _).1 hx) : x ∈ S₂)
 #align subalgebra.star_closure_le Subalgebra.starClosure_le
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.star_closure_le_iff Subalgebra.starClosure_le_iffₓ'. -/
 theorem starClosure_le_iff {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} :
     S₁.starClosure ≤ S₂ ↔ S₁ ≤ S₂.toSubalgebra :=
   ⟨fun h => le_sup_left.trans h, starClosure_le⟩
@@ -701,12 +500,6 @@ theorem star_self_mem_adjoin_singleton (x : A) : star x ∈ adjoin R ({x} : Set
 
 variable {R}
 
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.gc StarSubalgebra.gcₓ'. -/
 protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A) coe :=
   by
   intro s S
@@ -716,12 +509,6 @@ protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A
       Set.union_subset h fun x hx => star_star x ▸ star_mem (show star x ∈ S from h hx)⟩
 #align star_subalgebra.gc StarSubalgebra.gc
 
-/- warning: star_subalgebra.gi -> StarSubalgebra.gi is a dubious translation:
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 /-- Galois insertion between `adjoin` and `coe`. -/
 protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) coe
     where
@@ -731,41 +518,20 @@ protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) coe
   choice_eq _ _ := StarSubalgebra.copy_eq _ _ _
 #align star_subalgebra.gi StarSubalgebra.gi
 
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 theorem adjoin_le {S : StarSubalgebra R A} {s : Set A} (hs : s ⊆ S) : adjoin R s ≤ S :=
   StarSubalgebra.gc.l_le hs
 #align star_subalgebra.adjoin_le StarSubalgebra.adjoin_le
 
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 theorem adjoin_le_iff {S : StarSubalgebra R A} {s : Set A} : adjoin R s ≤ S ↔ s ⊆ S :=
   StarSubalgebra.gc _ _
 #align star_subalgebra.adjoin_le_iff StarSubalgebra.adjoin_le_iff
 
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-Case conversion may be inaccurate. Consider using '#align subalgebra.star_closure_eq_adjoin Subalgebra.starClosure_eq_adjoinₓ'. -/
 theorem Subalgebra.starClosure_eq_adjoin (S : Subalgebra R A) :
     S.starClosure = adjoin R (S : Set A) :=
   le_antisymm (Subalgebra.starClosure_le_iff.2 <| subset_adjoin R (S : Set A))
     (adjoin_le (le_sup_left : S ≤ S ⊔ star S))
 #align subalgebra.star_closure_eq_adjoin Subalgebra.starClosure_eq_adjoin
 
-/- warning: star_subalgebra.adjoin_induction -> StarSubalgebra.adjoin_induction is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_inductionₓ'. -/
 /-- If some predicate holds for all `x ∈ (s : set A)` and this predicate is closed under the
 `algebra_map`, addition, multiplication and star operations, then it holds for `a ∈ adjoin R s`. -/
 theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin R s)
@@ -777,9 +543,6 @@ theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin
     Hmul
 #align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_induction
 
-/- warning: star_subalgebra.adjoin_induction₂ -> StarSubalgebra.adjoin_induction₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂ₓ'. -/
 theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a ∈ adjoin R s)
     (hb : b ∈ adjoin R s) (Hs : ∀ x : A, x ∈ s → ∀ y : A, y ∈ s → p x y)
     (Halg : ∀ r₁ r₂ : R, p (algebraMap R A r₁) (algebraMap R A r₂))
@@ -803,9 +566,6 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
   · cases hx; exacts[Halg_right _ _ hx, star_star x ▸ Hstar_left _ _ (Halg_right r _ hx)]
 #align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂
 
-/- warning: star_subalgebra.adjoin_induction' -> StarSubalgebra.adjoin_induction' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction' StarSubalgebra.adjoin_induction'ₓ'. -/
 /-- The difference with `star_subalgebra.adjoin_induction` is that this acts on the subtype. -/
 theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
     (Hs : ∀ (x) (h : x ∈ s), p ⟨x, subset_adjoin R s h⟩) (Halg : ∀ r, p (algebraMap R _ r))
@@ -825,12 +585,6 @@ theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
 
 variable (R)
 
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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)))
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_comm_semiring_of_comm StarSubalgebra.adjoinCommSemiringOfCommₓ'. -/
 /-- If all elements of `s : set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `star_subalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
 @[reducible]
@@ -854,12 +608,6 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
       exact congr_arg coe (mul_comm (⟨x, hx⟩ : Algebra.adjoin R (s ∪ star s)) ⟨y, hy⟩) }
 #align star_subalgebra.adjoin_comm_semiring_of_comm StarSubalgebra.adjoinCommSemiringOfComm
 
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_comm_ring_of_comm StarSubalgebra.adjoinCommRingOfCommₓ'. -/
 /-- If all elements of `s : set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `star_subalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
 @[reducible]
@@ -872,12 +620,6 @@ def adjoinCommRingOfComm (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ri
     (adjoin R s).toSubalgebra.toRing with }
 #align star_subalgebra.adjoin_comm_ring_of_comm StarSubalgebra.adjoinCommRingOfComm
 
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormalₓ'. -/
 /-- The star subalgebra `star_subalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
 instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
@@ -887,12 +629,6 @@ instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
     simpa only [ha, hb] using (star_comm_self' x).symm
 #align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormal
 
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 /-- The star subalgebra `star_subalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
 instance adjoinCommRingOfIsStarNormal (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ring A]
@@ -912,222 +648,102 @@ instance : CompleteLattice (StarSubalgebra R A) :=
 instance : Inhabited (StarSubalgebra R A) :=
   ⟨⊤⟩
 
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 @[simp]
 theorem coe_top : (↑(⊤ : StarSubalgebra R A) : Set A) = Set.univ :=
   rfl
 #align star_subalgebra.coe_top StarSubalgebra.coe_top
 
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 @[simp]
 theorem mem_top {x : A} : x ∈ (⊤ : StarSubalgebra R A) :=
   Set.mem_univ x
 #align star_subalgebra.mem_top StarSubalgebra.mem_top
 
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 @[simp]
 theorem top_toSubalgebra : (⊤ : StarSubalgebra R A).toSubalgebra = ⊤ :=
   rfl
 #align star_subalgebra.top_to_subalgebra StarSubalgebra.top_toSubalgebra
 
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 @[simp]
 theorem toSubalgebra_eq_top {S : StarSubalgebra R A} : S.toSubalgebra = ⊤ ↔ S = ⊤ :=
   StarSubalgebra.toSubalgebra_injective.eq_iff' top_toSubalgebra
 #align star_subalgebra.to_subalgebra_eq_top StarSubalgebra.toSubalgebra_eq_top
 
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_sup_left StarSubalgebra.mem_sup_leftₓ'. -/
 theorem mem_sup_left {S T : StarSubalgebra R A} : ∀ {x : A}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
 #align star_subalgebra.mem_sup_left StarSubalgebra.mem_sup_left
 
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_sup_right StarSubalgebra.mem_sup_rightₓ'. -/
 theorem mem_sup_right {S T : StarSubalgebra R A} : ∀ {x : A}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
 #align star_subalgebra.mem_sup_right StarSubalgebra.mem_sup_right
 
-/- warning: star_subalgebra.mul_mem_sup -> StarSubalgebra.mul_mem_sup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mul_mem_sup StarSubalgebra.mul_mem_supₓ'. -/
 theorem mul_mem_sup {S T : StarSubalgebra R A} {x y : A} (hx : x ∈ S) (hy : y ∈ T) :
     x * y ∈ S ⊔ T :=
   mul_mem (mem_sup_left hx) (mem_sup_right hy)
 #align star_subalgebra.mul_mem_sup StarSubalgebra.mul_mem_sup
 
-/- warning: star_subalgebra.map_sup -> StarSubalgebra.map_sup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_sup StarSubalgebra.map_supₓ'. -/
 theorem map_sup (f : A →⋆ₐ[R] B) (S T : StarSubalgebra R A) : map f (S ⊔ T) = map f S ⊔ map f T :=
   (StarSubalgebra.gc_map_comap f).l_sup
 #align star_subalgebra.map_sup StarSubalgebra.map_sup
 
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 @[simp, norm_cast]
 theorem coe_inf (S T : StarSubalgebra R A) : (↑(S ⊓ T) : Set A) = S ∩ T :=
   rfl
 #align star_subalgebra.coe_inf StarSubalgebra.coe_inf
 
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 @[simp]
 theorem mem_inf {S T : StarSubalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x ∈ T :=
   Iff.rfl
 #align star_subalgebra.mem_inf StarSubalgebra.mem_inf
 
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 @[simp]
 theorem inf_toSubalgebra (S T : StarSubalgebra R A) :
     (S ⊓ T).toSubalgebra = S.toSubalgebra ⊓ T.toSubalgebra :=
   rfl
 #align star_subalgebra.inf_to_subalgebra StarSubalgebra.inf_toSubalgebra
 
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 @[simp, norm_cast]
 theorem coe_sInf (S : Set (StarSubalgebra R A)) : (↑(sInf S) : Set A) = ⋂ s ∈ S, ↑s :=
   sInf_image
 #align star_subalgebra.coe_Inf StarSubalgebra.coe_sInf
 
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-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_Inf StarSubalgebra.mem_sInfₓ'. -/
 theorem mem_sInf {S : Set (StarSubalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p := by
   simp only [← SetLike.mem_coe, coe_Inf, Set.mem_iInter₂]
 #align star_subalgebra.mem_Inf StarSubalgebra.mem_sInf
 
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 @[simp]
 theorem sInf_toSubalgebra (S : Set (StarSubalgebra R A)) :
     (sInf S).toSubalgebra = sInf (StarSubalgebra.toSubalgebra '' S) :=
   SetLike.coe_injective <| by simp
 #align star_subalgebra.Inf_to_subalgebra StarSubalgebra.sInf_toSubalgebra
 
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 @[simp, norm_cast]
 theorem coe_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
   simp [iInf]
 #align star_subalgebra.coe_infi StarSubalgebra.coe_iInf
 
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 theorem mem_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} {x : A} :
     (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [iInf, mem_Inf, Set.forall_range_iff]
 #align star_subalgebra.mem_infi StarSubalgebra.mem_iInf
 
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 @[simp]
 theorem iInf_toSubalgebra {ι : Sort _} (S : ι → StarSubalgebra R A) :
     (⨅ i, S i).toSubalgebra = ⨅ i, (S i).toSubalgebra :=
   SetLike.coe_injective <| by simp
 #align star_subalgebra.infi_to_subalgebra StarSubalgebra.iInf_toSubalgebra
 
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 theorem bot_toSubalgebra : (⊥ : StarSubalgebra R A).toSubalgebra = ⊥ := by
   change Algebra.adjoin R (∅ ∪ star ∅) = Algebra.adjoin R ∅; simp
 #align star_subalgebra.bot_to_subalgebra StarSubalgebra.bot_toSubalgebra
 
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 theorem mem_bot {x : A} : x ∈ (⊥ : StarSubalgebra R A) ↔ x ∈ Set.range (algebraMap R A) := by
   rw [← mem_to_subalgebra, bot_to_subalgebra, Algebra.mem_bot]
 #align star_subalgebra.mem_bot StarSubalgebra.mem_bot
 
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 @[simp]
 theorem coe_bot : ((⊥ : StarSubalgebra R A) : Set A) = Set.range (algebraMap R A) := by
   simp [Set.ext_iff, mem_bot]
 #align star_subalgebra.coe_bot StarSubalgebra.coe_bot
 
-/- warning: star_subalgebra.eq_top_iff -> StarSubalgebra.eq_top_iff is a dubious translation:
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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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S (Top.top.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (forall (x : A), Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (Eq.{succ u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S (Top.top.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (forall (x : A), Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x S)
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.eq_top_iff StarSubalgebra.eq_top_iffₓ'. -/
 theorem eq_top_iff {S : StarSubalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=
   ⟨fun h x => by rw [h] <;> exact mem_top, fun h => by
     ext x <;> exact ⟨fun _ => mem_top, fun _ => h x⟩⟩
@@ -1163,42 +779,27 @@ def equalizer : StarSubalgebra R A
 #align star_alg_hom.equalizer StarAlgHom.equalizer
 -/
 
-/- warning: star_alg_hom.mem_equalizer -> StarAlgHom.mem_equalizer is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
   Iff.rfl
 #align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizer
 
-/- warning: star_alg_hom.adjoin_le_equalizer -> StarAlgHom.adjoin_le_equalizer is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
 #align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizer
 
-/- warning: star_alg_hom.ext_of_adjoin_eq_top -> StarAlgHom.ext_of_adjoin_eq_top is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
 #align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_top
 
 omit hF
 
-/- warning: star_alg_hom.map_adjoin -> StarAlgHom.map_adjoin is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
   GaloisConnection.l_comm_of_u_comm Set.image_preimage (gc_map_comap f) StarSubalgebra.gc
     StarSubalgebra.gc fun _ => rfl
 #align star_alg_hom.map_adjoin StarAlgHom.map_adjoin
 
-/- warning: star_alg_hom.ext_adjoin -> StarAlgHom.ext_adjoin is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
   by
@@ -1213,9 +814,6 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
   · rw [map_star, map_star, hx]
 #align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoin
 
-/- warning: star_alg_hom.ext_adjoin_singleton -> StarAlgHom.ext_adjoin_singleton is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=
   ext_adjoin fun x hx =>

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

@@ -799,10 +799,8 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
     exacts[Hs x hx y hy, star_star y ▸ Hstar_right _ _ (Hs _ hx _ hy),
       star_star x ▸ Hstar_left _ _ (Hs _ hx _ hy),
       star_star x ▸ star_star y ▸ Hstar _ _ (Hs _ hx _ hy)]
-  · cases hx
-    exacts[Halg_left _ _ hx, star_star x ▸ Hstar_right _ _ (Halg_left r _ hx)]
-  · cases hx
-    exacts[Halg_right _ _ hx, star_star x ▸ Hstar_left _ _ (Halg_right r _ hx)]
+  · cases hx; exacts[Halg_left _ _ hx, star_star x ▸ Hstar_right _ _ (Halg_left r _ hx)]
+  · cases hx; exacts[Halg_right _ _ hx, star_star x ▸ Hstar_left _ _ (Halg_right r _ hx)]
 #align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂
 
 /- warning: star_subalgebra.adjoin_induction' -> StarSubalgebra.adjoin_induction' is a dubious translation:
@@ -884,12 +882,8 @@ Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin
 if `x` is normal. -/
 instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
     CommSemiring (adjoin R ({x} : Set A)) :=
-  adjoinCommSemiringOfComm R
-    (fun a ha b hb => by
-      rw [Set.mem_singleton_iff] at ha hb
-      rw [ha, hb])
-    fun a ha b hb => by
-    rw [Set.mem_singleton_iff] at ha hb
+  adjoinCommSemiringOfComm R (fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb; rw [ha, hb])
+    fun a ha b hb => by rw [Set.mem_singleton_iff] at ha hb;
     simpa only [ha, hb] using (star_comm_self' x).symm
 #align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormal
 
@@ -1103,10 +1097,8 @@ lean 3 declaration is
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)], Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.bot_to_subalgebra StarSubalgebra.bot_toSubalgebraₓ'. -/
-theorem bot_toSubalgebra : (⊥ : StarSubalgebra R A).toSubalgebra = ⊥ :=
-  by
-  change Algebra.adjoin R (∅ ∪ star ∅) = Algebra.adjoin R ∅
-  simp
+theorem bot_toSubalgebra : (⊥ : StarSubalgebra R A).toSubalgebra = ⊥ := by
+  change Algebra.adjoin R (∅ ∪ star ∅) = Algebra.adjoin R ∅; simp
 #align star_subalgebra.bot_to_subalgebra StarSubalgebra.bot_toSubalgebra
 
 /- warning: star_subalgebra.mem_bot -> StarSubalgebra.mem_bot is a dubious translation:

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

@@ -240,10 +240,7 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 -/
 
 /- warning: star_subalgebra.coe_subtype -> StarSubalgebra.coe_subtype 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} ((fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A 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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
@@ -251,20 +248,14 @@ theorem coe_subtype : (S.Subtype : S → A) = coe :=
 #align star_subalgebra.coe_subtype StarSubalgebra.coe_subtype
 
 /- warning: star_subalgebra.subtype_apply -> StarSubalgebra.subtype_apply is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
 #align star_subalgebra.subtype_apply StarSubalgebra.subtype_apply
 
 /- warning: star_subalgebra.to_subalgebra_subtype -> StarSubalgebra.toSubalgebra_subtype is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.to_subalgebra_subtype StarSubalgebra.toSubalgebra_subtypeₓ'. -/
 @[simp]
 theorem toSubalgebra_subtype : S.toSubalgebra.val = S.Subtype.toAlgHom :=
@@ -272,10 +263,7 @@ theorem toSubalgebra_subtype : S.toSubalgebra.val = S.Subtype.toAlgHom :=
 #align star_subalgebra.to_subalgebra_subtype StarSubalgebra.toSubalgebra_subtype
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion StarSubalgebra.inclusionₓ'. -/
 /-- The inclusion map between `star_subalgebra`s given by `subtype.map id` as a `star_alg_hom`. -/
 @[simps]
@@ -291,10 +279,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 #align star_subalgebra.inclusion StarSubalgebra.inclusion
 
 /- warning: star_subalgebra.inclusion_injective -> StarSubalgebra.inclusion_injective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
@@ -302,10 +287,7 @@ theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 #align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injective
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_comp_inclusion StarSubalgebra.subtype_comp_inclusionₓ'. -/
 @[simp]
 theorem subtype_comp_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
@@ -326,20 +308,14 @@ def map (f : A →⋆ₐ[R] B) (S : StarSubalgebra R A) : StarSubalgebra R B :=
 -/
 
 /- warning: star_subalgebra.map_mono -> StarSubalgebra.map_mono is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_mono StarSubalgebra.map_monoₓ'. -/
 theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁ ≤ S₂ → S₁.map f ≤ S₂.map f :=
   Set.image_subset f
 #align star_subalgebra.map_mono StarSubalgebra.map_mono
 
 /- warning: star_subalgebra.map_injective -> StarSubalgebra.map_injective is a dubious translation:
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(StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
@@ -358,10 +334,7 @@ theorem map_id (S : StarSubalgebra R A) : S.map (StarAlgHom.id R A) = S :=
 #align star_subalgebra.map_id StarSubalgebra.map_id
 
 /- warning: star_subalgebra.map_map -> StarSubalgebra.map_map 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] [_inst_11 : Semiring.{u4} C] [_inst_12 : StarRing.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)] [_inst_13 : Algebra.{u1, u4} R C _inst_1 _inst_11] [_inst_14 : StarModule.{u1, u4} R C (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.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12))) (SMulZeroClass.toHasSmul.{u1, u4} R C (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R C (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R C (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (Module.toMulActionWithZero.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_11 _inst_13)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (g : StarAlgHom.{u1, u3, u4} R B C _inst_1 _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toHasStar.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12)))) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u4} (StarSubalgebra.{u1, u4} R C _inst_1 _inst_2 _inst_11 _inst_12 _inst_13 _inst_14) (StarSubalgebra.map.{u1, u3, u4} R B C _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 g (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (StarSubalgebra.map.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_11 _inst_12 _inst_13 _inst_14 (StarAlgHom.comp.{u1, u2, u3, u4} R A B C _inst_1 _inst_3 _inst_5 (InvolutiveStar.toHasStar.{u2} A 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(Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12))) g f) S)
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(AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_4))) (Algebra.toSMul.{u4, u3} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u4, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u4, u2} R B (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u4, u2} R B _inst_1 _inst_7 _inst_9)] [_inst_11 : Semiring.{u1} C] [_inst_12 : StarRing.{u1} C (Semiring.toNonUnitalSemiring.{u1} C _inst_11)] [_inst_13 : Algebra.{u4, u1} R C _inst_1 _inst_11] [_inst_14 : StarModule.{u4, u1} R C (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} C (StarAddMonoid.toInvolutiveStar.{u1} C (AddMonoidWithOne.toAddMonoid.{u1} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} C (NonAssocSemiring.toAddCommMonoidWithOne.{u1} C (Semiring.toNonAssocSemiring.{u1} C _inst_11)))) (StarRing.toStarAddMonoid.{u1} C (Semiring.toNonUnitalSemiring.{u1} C _inst_11) _inst_12))) (Algebra.toSMul.{u4, u1} R C _inst_1 _inst_11 _inst_13)] (S : StarSubalgebra.{u4, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (g : StarAlgHom.{u4, u2, u1} R B C _inst_1 _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toStar.{u1} C (StarAddMonoid.toInvolutiveStar.{u1} C (AddMonoidWithOne.toAddMonoid.{u1} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} C (NonAssocSemiring.toAddCommMonoidWithOne.{u1} C (Semiring.toNonAssocSemiring.{u1} C _inst_11)))) (StarRing.toStarAddMonoid.{u1} C (Semiring.toNonUnitalSemiring.{u1} C _inst_11) _inst_12)))) (f : StarAlgHom.{u4, u3, u2} R A B _inst_1 _inst_3 _inst_5 (InvolutiveStar.toStar.{u3} A (StarAddMonoid.toInvolutiveStar.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toStar.{u1} C (StarAddMonoid.toInvolutiveStar.{u1} C (AddMonoidWithOne.toAddMonoid.{u1} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} C (NonAssocSemiring.toAddCommMonoidWithOne.{u1} C (Semiring.toNonAssocSemiring.{u1} C _inst_11)))) (StarRing.toStarAddMonoid.{u1} C (Semiring.toNonUnitalSemiring.{u1} C _inst_11) _inst_12))) g f) S)
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_map StarSubalgebra.map_mapₓ'. -/
 theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ[R] B) :
     (S.map f).map g = S.map (g.comp f) :=
@@ -369,10 +342,7 @@ theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ
 #align star_subalgebra.map_map StarSubalgebra.map_map
 
 /- warning: star_subalgebra.mem_map -> StarSubalgebra.mem_map is a dubious translation:
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: A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 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(Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B 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(StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
@@ -380,10 +350,7 @@ theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
 #align star_subalgebra.mem_map StarSubalgebra.mem_map
 
 /- warning: star_subalgebra.map_to_subalgebra -> StarSubalgebra.map_toSubalgebra is a dubious translation:
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(StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, Eq.{succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_7 _inst_9) (StarSubalgebra.toSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 _inst_7 _inst_9 (StarAlgHom.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) f) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_to_subalgebra StarSubalgebra.map_toSubalgebraₓ'. -/
 theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
     (S.map f).toSubalgebra = S.toSubalgebra.map f.toAlgHom :=
@@ -391,10 +358,7 @@ theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
 #align star_subalgebra.map_to_subalgebra StarSubalgebra.map_toSubalgebra
 
 /- warning: star_subalgebra.coe_map -> StarSubalgebra.coe_map is a dubious translation:
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(NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -410,10 +374,7 @@ def comap (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) : StarSubalgebra R A :
 -/
 
 /- warning: star_subalgebra.map_le_iff_le_comap -> StarSubalgebra.map_le_iff_le_comap 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {U : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10}, Iff (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toHasLe.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S) U) (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f U))
-but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {U : StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10}, Iff (LE.le.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S) U) (LE.le.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f U))
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_le_iff_le_comap StarSubalgebra.map_le_iff_le_comapₓ'. -/
 theorem map_le_iff_le_comap {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {U : StarSubalgebra R B} :
     map f S ≤ U ↔ S ≤ comap f U :=
@@ -421,20 +382,14 @@ theorem map_le_iff_le_comap {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {U :
 #align star_subalgebra.map_le_iff_le_comap StarSubalgebra.map_le_iff_le_comap
 
 /- warning: star_subalgebra.gc_map_comap -> StarSubalgebra.gc_map_comap is a dubious translation:
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A _inst_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R 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_inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f)
-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.gc_map_comap StarSubalgebra.gc_map_comapₓ'. -/
 theorem gc_map_comap (f : A →⋆ₐ[R] B) : GaloisConnection (map f) (comap f) := fun S U =>
   map_le_iff_le_comap
 #align star_subalgebra.gc_map_comap StarSubalgebra.gc_map_comap
 
 /- warning: star_subalgebra.comap_mono -> StarSubalgebra.comap_mono 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S₁ : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {S₂ : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toHasLe.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S₁ S₂) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
-but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] {S₁ : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {S₂ : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))}, (LE.le.{u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S₁ S₂) -> (LE.le.{u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_mono StarSubalgebra.comap_monoₓ'. -/
 theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
     S₁ ≤ S₂ → S₁.comap f ≤ S₂.comap f :=
@@ -442,10 +397,7 @@ theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
 #align star_subalgebra.comap_mono StarSubalgebra.comap_mono
 
 /- warning: star_subalgebra.comap_injective -> StarSubalgebra.comap_injective 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) 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(StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u3, succ u2} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
-but is expected to have type
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(Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} 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(StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
@@ -467,10 +419,7 @@ theorem comap_id (S : StarSubalgebra R A) : S.comap (StarAlgHom.id R A) = S :=
 #align star_subalgebra.comap_id StarSubalgebra.comap_id
 
 /- warning: star_subalgebra.comap_comap -> StarSubalgebra.comap_comap 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] [_inst_11 : Semiring.{u4} C] [_inst_12 : StarRing.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)] [_inst_13 : Algebra.{u1, u4} R C _inst_1 _inst_11] [_inst_14 : StarModule.{u1, u4} R C (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.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12))) (SMulZeroClass.toHasSmul.{u1, u4} R C (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R C (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R C (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (Module.toMulActionWithZero.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_11 _inst_13)))))] (S : StarSubalgebra.{u1, u4} R C _inst_1 _inst_2 _inst_11 _inst_12 _inst_13 _inst_14) (g : StarAlgHom.{u1, u3, u4} R B C _inst_1 _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toHasStar.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12)))) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f (StarSubalgebra.comap.{u1, u3, u4} R B C _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 g S)) (StarSubalgebra.comap.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_11 _inst_12 _inst_13 _inst_14 (StarAlgHom.comp.{u1, u2, u3, u4} R A B C _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toHasStar.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12))) g f) S)
-but is expected to have type
-  forall {R : Type.{u4}} {A : Type.{u1}} {B : Type.{u2}} {C : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : StarRing.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u4, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u4, u1} R A (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u4, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u4, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u4, u2} R B (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u4, u2} R B _inst_1 _inst_7 _inst_9)] [_inst_11 : Semiring.{u3} C] [_inst_12 : StarRing.{u3} C (Semiring.toNonUnitalSemiring.{u3} C _inst_11)] [_inst_13 : Algebra.{u4, u3} R C _inst_1 _inst_11] [_inst_14 : StarModule.{u4, u3} R C (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u3} C (StarAddMonoid.toInvolutiveStar.{u3} C (AddMonoidWithOne.toAddMonoid.{u3} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} C (NonAssocSemiring.toAddCommMonoidWithOne.{u3} C (Semiring.toNonAssocSemiring.{u3} C _inst_11)))) (StarRing.toStarAddMonoid.{u3} C (Semiring.toNonUnitalSemiring.{u3} C _inst_11) _inst_12))) (Algebra.toSMul.{u4, u3} R C _inst_1 _inst_11 _inst_13)] (S : StarSubalgebra.{u4, u3} R C _inst_1 _inst_2 _inst_11 _inst_12 _inst_13 _inst_14) (g : StarAlgHom.{u4, u2, u3} R B C _inst_1 _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toStar.{u3} C (StarAddMonoid.toInvolutiveStar.{u3} C (AddMonoidWithOne.toAddMonoid.{u3} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} C (NonAssocSemiring.toAddCommMonoidWithOne.{u3} C (Semiring.toNonAssocSemiring.{u3} C _inst_11)))) (StarRing.toStarAddMonoid.{u3} C (Semiring.toNonUnitalSemiring.{u3} C _inst_11) _inst_12)))) (f : StarAlgHom.{u4, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (StarSubalgebra.{u4, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u4, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f (StarSubalgebra.comap.{u4, u2, u3} R B C _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 g S)) (StarSubalgebra.comap.{u4, u1, u3} R A C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_11 _inst_12 _inst_13 _inst_14 (StarAlgHom.comp.{u4, u1, u2, u3} R A B C _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toStar.{u3} C (StarAddMonoid.toInvolutiveStar.{u3} C (AddMonoidWithOne.toAddMonoid.{u3} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} C (NonAssocSemiring.toAddCommMonoidWithOne.{u3} C (Semiring.toNonAssocSemiring.{u3} C _inst_11)))) (StarRing.toStarAddMonoid.{u3} C (Semiring.toNonUnitalSemiring.{u3} C _inst_11) _inst_12))) g f) S)
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_comap StarSubalgebra.comap_comapₓ'. -/
 theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ[R] B) :
     (S.comap g).comap f = S.comap (g.comp f) :=
@@ -478,10 +427,7 @@ theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : A →
 #align star_subalgebra.comap_comap StarSubalgebra.comap_comap
 
 /- warning: star_subalgebra.mem_comap -> StarSubalgebra.mem_comap 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) S)
-but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B 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(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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -489,10 +435,7 @@ theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x 
 #align star_subalgebra.mem_comap StarSubalgebra.mem_comap
 
 /- warning: star_subalgebra.coe_comap -> StarSubalgebra.coe_comap is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
@@ -821,10 +764,7 @@ theorem Subalgebra.starClosure_eq_adjoin (S : Subalgebra R A) :
 #align subalgebra.star_closure_eq_adjoin Subalgebra.starClosure_eq_adjoin
 
 /- warning: star_subalgebra.adjoin_induction -> StarSubalgebra.adjoin_induction is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_inductionₓ'. -/
 /-- If some predicate holds for all `x ∈ (s : set A)` and this predicate is closed under the
 `algebra_map`, addition, multiplication and star operations, then it holds for `a ∈ adjoin R s`. -/
@@ -838,10 +778,7 @@ theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin
 #align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_induction
 
 /- warning: star_subalgebra.adjoin_induction₂ -> StarSubalgebra.adjoin_induction₂ is a dubious translation:
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(Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x) y)) -> (forall (x : A) (y : A), (p x y) -> (p x (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) y))) -> (p a b)
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂ₓ'. -/
 theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a ∈ adjoin R s)
     (hb : b ∈ adjoin R s) (Hs : ∀ x : A, x ∈ s → ∀ y : A, y ∈ s → p x y)
@@ -869,10 +806,7 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
 #align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂
 
 /- warning: star_subalgebra.adjoin_induction' -> StarSubalgebra.adjoin_induction' is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction' StarSubalgebra.adjoin_induction'ₓ'. -/
 /-- The difference with `star_subalgebra.adjoin_induction` is that this acts on the subtype. -/
 theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
@@ -1049,10 +983,7 @@ theorem mem_sup_right {S T : StarSubalgebra R A} : ∀ {x : A}, x ∈ T → x 
 #align star_subalgebra.mem_sup_right StarSubalgebra.mem_sup_right
 
 /- warning: star_subalgebra.mul_mem_sup -> StarSubalgebra.mul_mem_sup is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mul_mem_sup StarSubalgebra.mul_mem_supₓ'. -/
 theorem mul_mem_sup {S T : StarSubalgebra R A} {x y : A} (hx : x ∈ S) (hy : y ∈ T) :
     x * y ∈ S ⊔ T :=
@@ -1060,10 +991,7 @@ theorem mul_mem_sup {S T : StarSubalgebra R A} {x y : A} (hx : x ∈ S) (hy : y
 #align star_subalgebra.mul_mem_sup StarSubalgebra.mul_mem_sup
 
 /- warning: star_subalgebra.map_sup -> StarSubalgebra.map_sup is a dubious translation:
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_inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) 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StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (T : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (Sup.sup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeSup.toHasSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) S T)) (Sup.sup.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (SemilatticeSup.toHasSup.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (Lattice.toSemilatticeSup.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (ConditionallyCompleteLattice.toLattice.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (CompleteLattice.toConditionallyCompleteLattice.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.completeLattice.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10))))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f S) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f T))
-but is expected to have type
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_sup StarSubalgebra.map_supₓ'. -/
 theorem map_sup (f : A →⋆ₐ[R] B) (S T : StarSubalgebra R A) : map f (S ⊔ T) = map f S ⊔ map f T :=
   (StarSubalgebra.gc_map_comap f).l_sup
@@ -1244,10 +1172,7 @@ def equalizer : StarSubalgebra R A
 -/
 
 /- warning: star_alg_hom.mem_equalizer -> StarAlgHom.mem_equalizer is a dubious translation:
-lean 3 declaration is
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(AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A 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 Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
@@ -1255,20 +1180,14 @@ theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
 #align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizer
 
 /- warning: star_alg_hom.adjoin_le_equalizer -> StarAlgHom.adjoin_le_equalizer is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
 #align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizer
 
 /- warning: star_alg_hom.ext_of_adjoin_eq_top -> StarAlgHom.ext_of_adjoin_eq_top is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
@@ -1277,10 +1196,7 @@ theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (h
 omit hF
 
 /- warning: star_alg_hom.map_adjoin -> StarAlgHom.map_adjoin is a dubious translation:
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(NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B 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(Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B 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(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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B 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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
@@ -1289,10 +1205,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 #align star_alg_hom.map_adjoin StarAlgHom.map_adjoin
 
 /- warning: star_alg_hom.ext_adjoin -> StarAlgHom.ext_adjoin is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
@@ -1309,10 +1222,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
 #align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoin
 
 /- warning: star_alg_hom.ext_adjoin_singleton -> StarAlgHom.ext_adjoin_singleton is a dubious translation:
-lean 3 declaration is
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x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) (FunLike.coe.{succ u4, succ u2, succ u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
+<too large>
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=

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

@@ -243,7 +243,7 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} ((fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarAlgHom.hasCoeToFun.{u1, u2, u2} R (coeSort.{succ u2, 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(NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))))))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A 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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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_inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
@@ -254,7 +254,7 @@ theorem coe_subtype : (S.Subtype : S → A) = coe :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S), Eq.{succ u2} A (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R 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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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
@@ -294,7 +294,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) -> (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂)) (StarAlgHom.hasCoeToFun.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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(StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
@@ -339,7 +339,7 @@ theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u2, succ u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
@@ -372,7 +372,7 @@ theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => Exists.{0} (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (fun (H : Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) y)))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
@@ -394,7 +394,7 @@ theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -445,7 +445,7 @@ theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u3, succ u2} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
@@ -481,7 +481,7 @@ theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) S)
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -492,7 +492,7 @@ theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x 
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
@@ -1247,7 +1247,7 @@ def equalizer : StarSubalgebra R A
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.Mem.{u3, u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u4} B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f x) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g x))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
+  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
@@ -1258,7 +1258,7 @@ theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (LE.le.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toHasLe.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
@@ -1268,7 +1268,7 @@ theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAl
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {s : Set.{u3} A}, (Eq.{succ u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (Eq.{succ u1} F f g))
 but is expected to have type
-  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
+  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
@@ -1280,7 +1280,7 @@ omit hF
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_8)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (s : Set.{u2} A), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) f) s))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
@@ -1292,7 +1292,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {s : Set.{u3} A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A 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x))) -> (Eq.{succ u1} F f g)
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
+  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
@@ -1312,7 +1312,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 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_inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u1} F f g)
 but is expected to have type
-  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) 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_inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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+  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) 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(Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) 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(StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) (FunLike.coe.{succ u4, succ u2, succ u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3328 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -264,7 +264,7 @@ theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_5)) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_3 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_5) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarAlgHom.toAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5)) x (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_5) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarAlgHom.toAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5)) x (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_3 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_5) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarAlgHom.toAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.to_subalgebra_subtype StarSubalgebra.toSubalgebra_subtypeₓ'. -/
 @[simp]
 theorem toSubalgebra_subtype : S.toSubalgebra.val = S.Subtype.toAlgHom :=

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

@@ -192,7 +192,7 @@ variable (S : StarSubalgebra R A)
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (r : R), Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5) r) S
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5) r) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5) r) S
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.algebra_map_mem StarSubalgebra.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
   S.algebraMap_mem' r
@@ -212,7 +212,7 @@ theorem rangeS_le : (algebraMap R A).srange ≤ S.toSubalgebra.toSubsemiring :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5))) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S)
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5))) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5))) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.range_subset StarSubalgebra.range_subsetₓ'. -/
 theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ => hr ▸ S.algebraMap_mem r
 #align star_subalgebra.range_subset StarSubalgebra.range_subset
@@ -221,7 +221,7 @@ theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ =>
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), LE.le.{u2} (Set.{u2} A) (Set.hasLe.{u2} A) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5))) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S)
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), LE.le.{u2} (Set.{u2} A) (Set.instLESet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5))) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), LE.le.{u2} (Set.{u2} A) (Set.instLESet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5))) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.range_le StarSubalgebra.range_leₓ'. -/
 theorem range_le : Set.range (algebraMap R A) ≤ S :=
   S.range_subset
@@ -824,7 +824,7 @@ theorem Subalgebra.starClosure_eq_adjoin (S : Subalgebra R A) :
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {s : Set.{u2} A} {p : A -> Prop} {a : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) a (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (forall (x : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (p x)) -> (forall (r : R), p (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r)) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x y))) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x y))) -> (forall (x : A), (p x) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x))) -> (p a)
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {s : Set.{u2} A} {p : A -> Prop} {a : A}, (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) a (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (forall (x : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s) -> (p x)) -> (forall (r : R), p (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r)) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x y))) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) x y))) -> (forall (x : A), (p x) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x))) -> (p a)
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {s : Set.{u2} A} {p : A -> Prop} {a : A}, (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) a (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (forall (x : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s) -> (p x)) -> (forall (r : R), p (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r)) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x y))) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) x y))) -> (forall (x : A), (p x) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x))) -> (p a)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_inductionₓ'. -/
 /-- If some predicate holds for all `x ∈ (s : set A)` and this predicate is closed under the
 `algebra_map`, addition, multiplication and star operations, then it holds for `a ∈ adjoin R s`. -/
@@ -841,7 +841,7 @@ theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {s : Set.{u2} A} {p : A -> A -> Prop} {a : A} {b : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) a (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) b (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (forall (x : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (forall (y : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) y s) -> (p x y))) -> (forall (r₁ : R) (r₂ : R), p (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r₁) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r₂)) -> (forall (r : R) (x : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (p 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(Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r))) -> (forall (x₁ : A) (x₂ : A) (y : A), (p x₁ y) -> (p x₂ y) -> (p (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x₁ x₂) y)) -> (forall (x : A) (y₁ : A) (y₂ : A), (p x y₁) -> (p x y₂) -> (p x (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) y₁ y₂))) -> (forall (x₁ : A) (x₂ : A) (y : A), (p x₁ y) -> (p x₂ y) -> (p (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x₁ x₂) y)) -> (forall (x : A) (y₁ : A) (y₂ : A), (p x y₁) -> (p x y₂) -> (p x (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) y₁ y₂))) -> (forall (x : A) (y : A), (p x y) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) y))) -> (forall (x : A) (y : A), (p x y) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x) y)) -> (forall (x : A) (y : A), (p x y) -> (p x (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) y))) -> (p a b)
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {s : Set.{u2} A} {p : A -> A -> Prop} {a : A} {b : A}, (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) a (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) b (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (forall (x : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s) -> (forall (y : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) y s) -> (p x y))) -> (forall (r₁ : R) (r₂ : R), p (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r₂)) -> (forall (r : R) (x : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s) -> (p (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r) x)) -> (forall (r : R) (x : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s) -> (p x (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r))) -> (forall (x₁ : A) (x₂ : A) (y : A), (p x₁ y) -> (p x₂ y) -> (p (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x₁ x₂) y)) -> (forall (x : A) (y₁ : A) (y₂ : A), (p x y₁) -> (p x y₂) -> (p x (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) y₁ y₂))) -> (forall (x₁ : A) (x₂ : A) (y : A), (p x₁ y) -> (p x₂ y) -> (p (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) x₁ x₂) y)) -> (forall (x : A) (y₁ : A) (y₂ : A), (p x y₁) -> (p x y₂) -> (p x (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) y₁ y₂))) -> (forall (x : A) (y : A), (p x y) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) y))) -> (forall (x : A) (y : A), (p x y) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x) y)) -> (forall (x : A) (y : A), (p x y) -> (p x (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) y))) -> (p a b)
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {s : Set.{u2} A} {p : A -> A -> Prop} {a : A} {b : A}, (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) a (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) b (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (forall (x : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s) -> (forall (y : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) y s) -> (p x y))) -> (forall (r₁ : R) (r₂ : R), p (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r₂)) -> (forall (r : R) (x : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s) -> (p (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r) x)) -> (forall (r : R) (x : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s) -> (p x (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r))) -> (forall (x₁ : A) (x₂ : A) (y : A), (p x₁ y) -> (p x₂ y) -> (p (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x₁ x₂) y)) -> (forall (x : A) (y₁ : A) (y₂ : A), (p x y₁) -> (p x y₂) -> (p x (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) y₁ y₂))) -> (forall (x₁ : A) (x₂ : A) (y : A), (p x₁ y) -> (p x₂ y) -> (p (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) x₁ x₂) y)) -> (forall (x : A) (y₁ : A) (y₂ : A), (p x y₁) -> (p x y₂) -> (p x (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) y₁ y₂))) -> (forall (x : A) (y : A), (p x y) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) y))) -> (forall (x : A) (y : A), (p x y) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x) y)) -> (forall (x : A) (y : A), (p x y) -> (p x (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) y))) -> (p a b)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂ₓ'. -/
 theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a ∈ adjoin R s)
     (hb : b ∈ adjoin R s) (Hs : ∀ x : A, x ∈ s → ∀ y : A, y ∈ s → p x y)
@@ -872,7 +872,7 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {s : Set.{u2} A} {p : (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> Prop} (a : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)), (forall (x : A) (h : Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s), p (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A 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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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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 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_inst_5 _inst_6 s))), (p x) -> (p (Star.star.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 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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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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 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_inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)))))))) (algebraMap.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) r)) -> (forall (x : Subtype.{succ u2} A (fun (x : A) => 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_inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (instHAdd.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Distrib.toAdd.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subsemiring.toNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)))))))) x y))) -> (forall (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (y : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (p x) -> (p y) -> (p (HMul.hMul.{u2, u2, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Submonoid.mul.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Subsemiring.toSubmonoid.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)))))) x y))) -> (forall (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (p x) -> (p (Star.star.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) x))) -> (p a)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction' StarSubalgebra.adjoin_induction'ₓ'. -/
 /-- The difference with `star_subalgebra.adjoin_induction` is that this acts on the subtype. -/
 theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
@@ -1185,7 +1185,7 @@ theorem bot_toSubalgebra : (⊥ : StarSubalgebra R A).toSubalgebra = ⊥ :=
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {x : A}, Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4))))
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {x : A}, Iff (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4))))
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {x : A}, Iff (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4))))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_bot StarSubalgebra.mem_botₓ'. -/
 theorem mem_bot {x : A} : x ∈ (⊥ : StarSubalgebra R A) ↔ x ∈ Set.range (algebraMap R A) := by
   rw [← mem_to_subalgebra, bot_to_subalgebra, Algebra.mem_bot]
@@ -1195,7 +1195,7 @@ theorem mem_bot {x : A} : x ∈ (⊥ : StarSubalgebra R A) ↔ x ∈ Set.range (
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))], 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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)], Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)], Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_bot StarSubalgebra.coe_botₓ'. -/
 @[simp]
 theorem coe_bot : ((⊥ : StarSubalgebra R A) : Set A) = Set.range (algebraMap R A) := by

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

@@ -926,7 +926,7 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13))] [_inst_16 : 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_11)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11))) _inst_12))) (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) (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_13))))))) (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_11)))))) (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_13))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11))) (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_13))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)))))] {s : Set.{u2} A}, (forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (forall (b : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13))) a b) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13))) b a)))) -> (forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (forall (b : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13))) a (Star.star.{u2} A (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) b)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13))) (Star.star.{u2} A (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) b) a)))) -> (CommRing.{u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 s)))
 but is expected to have type
-  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))] [_inst_16 : 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_11)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11))) _inst_12))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)] {s : Set.{u2} A}, (forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (forall (b : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))))) a b) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))))) b a)))) -> (forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (forall (b : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))))) a (Star.star.{u2} A (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) b)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))))) (Star.star.{u2} A (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) b) a)))) -> (CommRing.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) x (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 s))))
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))] [_inst_16 : 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_11)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11))) _inst_12))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)] {s : Set.{u2} A}, (forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (forall (b : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_13)))) a b) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_13)))) b a)))) -> (forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (forall (b : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_13)))) a (Star.star.{u2} A (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) b)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_13)))) (Star.star.{u2} A (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) b) a)))) -> (CommRing.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) x (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 s))))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_comm_ring_of_comm StarSubalgebra.adjoinCommRingOfCommₓ'. -/
 /-- If all elements of `s : set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `star_subalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
@@ -963,7 +963,7 @@ instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
 lean 3 declaration is
   forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13))] [_inst_16 : 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_11)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11))) _inst_12))) (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) (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_13))))))) (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_11)))))) (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_13))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11))) (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_13))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)))))] (x : A) [_inst_17 : IsStarNormal.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13)) (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) x], CommRing.{u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) x)))
 but is expected to have type
-  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))] [_inst_16 : 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_11)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11))) _inst_12))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)] (x : A) [_inst_17 : IsStarNormal.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) x], CommRing.{u2} (Subtype.{succ u2} A (fun (x_1 : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) x_1 (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) x))))
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))] [_inst_16 : 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_11)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11))) _inst_12))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)] (x : A) [_inst_17 : IsStarNormal.{u2} A (NonUnitalNonAssocRing.toMul.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A _inst_13))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) x], CommRing.{u2} (Subtype.{succ u2} A (fun (x_1 : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) x_1 (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) x))))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_comm_ring_of_is_star_normal StarSubalgebra.adjoinCommRingOfIsStarNormalₓ'. -/
 /-- The star subalgebra `star_subalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/

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

@@ -143,7 +143,7 @@ theorem toSubalgebra_inj {S U : StarSubalgebra R A} : S.toSubalgebra = U.toSubal
 
 /- warning: star_subalgebra.to_subalgebra_le_iff -> StarSubalgebra.toSubalgebra_le_iff 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, Iff (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_5))))) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, Iff (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_5))))) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂)
 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, Iff (LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5))))) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.to_subalgebra_le_iff StarSubalgebra.toSubalgebra_le_iffₓ'. -/
@@ -200,7 +200,7 @@ theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
 
 /- warning: star_subalgebra.srange_le -> StarSubalgebra.rangeS_le 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), LE.le.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Preorder.toLE.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (PartialOrder.toPreorder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Subsemiring.completeLattice.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (RingHom.rangeS.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), LE.le.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Preorder.toHasLe.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (PartialOrder.toPreorder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Subsemiring.completeLattice.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (RingHom.rangeS.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), LE.le.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Preorder.toLE.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (PartialOrder.toPreorder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Subsemiring.instCompleteLatticeSubsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (RingHom.rangeS.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.srange_le StarSubalgebra.rangeS_leₓ'. -/
@@ -273,7 +273,7 @@ theorem toSubalgebra_subtype : S.toSubalgebra.val = S.Subtype.toAlgHom :=
 
 /- warning: star_subalgebra.inclusion -> StarSubalgebra.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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂))
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion StarSubalgebra.inclusionₓ'. -/
@@ -292,7 +292,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 
 /- warning: star_subalgebra.inclusion_injective -> StarSubalgebra.inclusion_injective 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 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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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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 but is expected to have type
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A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 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_inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) 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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
@@ -303,7 +303,7 @@ theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂)
 
 /- warning: star_subalgebra.subtype_comp_inclusion -> StarSubalgebra.subtype_comp_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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Eq.{succ u2} (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarAlgHom.comp.{u1, u2, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h)) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Eq.{succ u2} (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarAlgHom.comp.{u1, u2, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h)) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)
 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Eq.{succ 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) A _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4)))) (StarAlgHom.comp.{u2, u1, 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) A _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h)) (StarSubalgebra.subtype.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_comp_inclusion StarSubalgebra.subtype_comp_inclusionₓ'. -/
@@ -327,7 +327,7 @@ def map (f : A →⋆ₐ[R] B) (S : StarSubalgebra R A) : StarSubalgebra R B :=
 
 /- warning: star_subalgebra.map_mono -> StarSubalgebra.map_mono 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toHasLe.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
 but is expected to have type
   forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S₁ : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (LE.le.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (LE.le.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_mono StarSubalgebra.map_monoₓ'. -/
@@ -411,7 +411,7 @@ def comap (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) : StarSubalgebra R A :
 
 /- warning: star_subalgebra.map_le_iff_le_comap -> StarSubalgebra.map_le_iff_le_comap 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {U : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10}, Iff (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S) U) (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f U))
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {U : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10}, Iff (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toHasLe.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S) U) (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f U))
 but is expected to have type
   forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {U : StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10}, Iff (LE.le.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S) U) (LE.le.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f U))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_le_iff_le_comap StarSubalgebra.map_le_iff_le_comapₓ'. -/
@@ -432,7 +432,7 @@ theorem gc_map_comap (f : A →⋆ₐ[R] B) : GaloisConnection (map f) (comap f)
 
 /- warning: star_subalgebra.comap_mono -> StarSubalgebra.comap_mono 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S₁ : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {S₂ : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S₁ S₂) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S₁ : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {S₂ : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toHasLe.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S₁ S₂) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
 but is expected to have type
   forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] {S₁ : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {S₂ : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))}, (LE.le.{u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S₁ S₂) -> (LE.le.{u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_mono StarSubalgebra.comap_monoₓ'. -/
@@ -549,7 +549,7 @@ theorem mem_centralizer_iff {s : Set A} {w} {z : A} :
 
 /- warning: star_subalgebra.centralizer_le -> StarSubalgebra.centralizer_le 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (s : Set.{u2} A) (t : Set.{u2} A) (ws : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)) (wt : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a t) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) t)), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s t) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 t wt) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s ws))
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (s : Set.{u2} A) (t : Set.{u2} A) (ws : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)) (wt : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a t) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) t)), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s t) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 t wt) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s ws))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (s : Set.{u2} A) (t : Set.{u2} A) (ws : forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)) (wt : forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a t) -> (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) t)), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) s t) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 t wt) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s ws))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.centralizer_le StarSubalgebra.centralizer_leₓ'. -/
@@ -669,7 +669,7 @@ def starClosure (S : Subalgebra R A) : StarSubalgebra R A :=
 
 /- warning: subalgebra.star_closure_le -> Subalgebra.starClosure_le 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S₁ : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂)) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂)
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S₁ : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂)) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂)
 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S₁ : Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, (LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂)) -> (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂)
 Case conversion may be inaccurate. Consider using '#align subalgebra.star_closure_le Subalgebra.starClosure_leₓ'. -/
@@ -682,7 +682,7 @@ theorem starClosure_le {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} (h :
 
 /- warning: subalgebra.star_closure_le_iff -> Subalgebra.starClosure_le_iff 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S₁ : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂))
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S₁ : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Preorder.toHasLe.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂))
 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S₁ : Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂) (LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂))
 Case conversion may be inaccurate. Consider using '#align subalgebra.star_closure_le_iff Subalgebra.starClosure_le_iffₓ'. -/
@@ -790,7 +790,7 @@ protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) coe
 
 /- warning: star_subalgebra.adjoin_le -> StarSubalgebra.adjoin_le 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u2} A}, (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s ((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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) S)) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u2} A}, (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s ((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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) S)) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u1} A}, (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) s (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S)) -> (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_le StarSubalgebra.adjoin_leₓ'. -/
@@ -800,7 +800,7 @@ theorem adjoin_le {S : StarSubalgebra R A} {s : Set A} (hs : s ⊆ S) : adjoin R
 
 /- warning: star_subalgebra.adjoin_le_iff -> StarSubalgebra.adjoin_le_iff 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u2} A}, Iff (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) S) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s ((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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u2} A}, Iff (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toHasLe.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) S) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s ((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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u1} A}, Iff (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) S) (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) s (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_le_iff StarSubalgebra.adjoin_le_iffₓ'. -/
@@ -1256,7 +1256,7 @@ theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
 
 /- warning: star_alg_hom.adjoin_le_equalizer -> StarAlgHom.adjoin_le_equalizer is a dubious translation:
 lean 3 declaration is
-  forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (LE.le.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+  forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (LE.le.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toHasLe.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 but is expected to have type
   forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/

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

@@ -243,7 +243,7 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} ((fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarAlgHom.hasCoeToFun.{u1, u2, u2} R (coeSort.{succ u2, 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(NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))))))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A 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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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_inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
@@ -254,7 +254,7 @@ theorem coe_subtype : (S.Subtype : S → A) = coe :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S), Eq.{succ u2} A (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R 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 but is expected to have type
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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
@@ -294,7 +294,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) -> (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂)) (StarAlgHom.hasCoeToFun.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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(StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
@@ -339,7 +339,7 @@ theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u2, succ u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
@@ -372,7 +372,7 @@ theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => Exists.{0} (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (fun (H : Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) y)))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
@@ -394,7 +394,7 @@ theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -445,7 +445,7 @@ theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u3, succ u2} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
@@ -481,7 +481,7 @@ theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) S)
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -492,7 +492,7 @@ theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x 
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
@@ -1247,7 +1247,7 @@ def equalizer : StarSubalgebra R A
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.Mem.{u3, u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u4} B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f x) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g x))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
+  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
@@ -1258,7 +1258,7 @@ theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (LE.le.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
@@ -1268,7 +1268,7 @@ theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAl
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {s : Set.{u3} A}, (Eq.{succ u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (Eq.{succ u1} F f g))
 but is expected to have type
-  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
+  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
@@ -1280,7 +1280,7 @@ omit hF
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_8)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (s : Set.{u2} A), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) f) s))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
@@ -1292,7 +1292,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {s : Set.{u3} A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A 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x))) -> (Eq.{succ u1} F f g)
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
+  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
@@ -1312,7 +1312,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 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u3} A (Set.{u3} A) (Set.hasSingleton.{u3} A) a))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) _inst_10))) g (Subtype.mk.{succ u3} A (fun (x : A) => Membership.Mem.{u3, u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u3, u3} A (Set.{u3} A) (Set.hasSingleton.{u3} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u1} F f g)
 but is expected to have type
-  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) 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_inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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+  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) 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(Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) 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(StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 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x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) (FunLike.coe.{succ u4, succ u2, succ u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3326 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=

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

@@ -1103,71 +1103,71 @@ theorem inf_toSubalgebra (S T : StarSubalgebra R A) :
   rfl
 #align star_subalgebra.inf_to_subalgebra StarSubalgebra.inf_toSubalgebra
 
-/- warning: star_subalgebra.coe_Inf -> StarSubalgebra.coe_infₛ is a dubious translation:
+/- warning: star_subalgebra.coe_Inf -> StarSubalgebra.coe_sInf 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), 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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (Set.interᵢ.{u2, succ u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (fun (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) => Set.interᵢ.{u2, 0} A (Membership.Mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.hasMem.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) (fun (H : Membership.Mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.hasMem.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) => (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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), 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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (InfSet.sInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (Set.iInter.{u2, succ u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (fun (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) => Set.iInter.{u2, 0} A (Membership.Mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.hasMem.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) (fun (H : Membership.Mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.hasMem.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) => (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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) s)))
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (Set.interᵢ.{u2, succ u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (fun (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) => Set.interᵢ.{u2, 0} A (Membership.mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.instMembershipSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) (fun (H : Membership.mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.instMembershipSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) => SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) s)))
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_Inf StarSubalgebra.coe_infₛₓ'. -/
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InfSet.sInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (Set.iInter.{u2, succ u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (fun (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) => Set.iInter.{u2, 0} A (Membership.mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.instMembershipSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) (fun (H : Membership.mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.instMembershipSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) => SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) s)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_Inf StarSubalgebra.coe_sInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (StarSubalgebra R A)) : (↑(infₛ S) : Set A) = ⋂ s ∈ S, ↑s :=
-  infₛ_image
-#align star_subalgebra.coe_Inf StarSubalgebra.coe_infₛ
+theorem coe_sInf (S : Set (StarSubalgebra R A)) : (↑(sInf S) : Set A) = ⋂ s ∈ S, ↑s :=
+  sInf_image
+#align star_subalgebra.coe_Inf StarSubalgebra.coe_sInf
 
-/- warning: star_subalgebra.mem_Inf -> StarSubalgebra.mem_infₛ is a dubious translation:
+/- warning: star_subalgebra.mem_Inf -> StarSubalgebra.mem_sInf 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (forall (p : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), (Membership.Mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.hasMem.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) p S) -> (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x p))
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (InfSet.sInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (forall (p : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), (Membership.Mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.hasMem.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) p S) -> (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x p))
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (forall (p : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), (Membership.mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.instMembershipSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) p S) -> (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x p))
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_Inf StarSubalgebra.mem_infₛₓ'. -/
-theorem mem_infₛ {S : Set (StarSubalgebra R A)} {x : A} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p := by
-  simp only [← SetLike.mem_coe, coe_Inf, Set.mem_interᵢ₂]
-#align star_subalgebra.mem_Inf StarSubalgebra.mem_infₛ
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (InfSet.sInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (forall (p : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), (Membership.mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.instMembershipSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) p S) -> (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x p))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_Inf StarSubalgebra.mem_sInfₓ'. -/
+theorem mem_sInf {S : Set (StarSubalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p := by
+  simp only [← SetLike.mem_coe, coe_Inf, Set.mem_iInter₂]
+#align star_subalgebra.mem_Inf StarSubalgebra.mem_sInf
 
-/- warning: star_subalgebra.Inf_to_subalgebra -> StarSubalgebra.infₛ_toSubalgebra is a dubious translation:
+/- warning: star_subalgebra.Inf_to_subalgebra -> StarSubalgebra.sInf_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))) (Set.image.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (InfSet.sInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))) (Set.image.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S))
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4))) (Set.image.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S))
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.Inf_to_subalgebra StarSubalgebra.infₛ_toSubalgebraₓ'. -/
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (InfSet.sInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (InfSet.sInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4))) (Set.image.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.Inf_to_subalgebra StarSubalgebra.sInf_toSubalgebraₓ'. -/
 @[simp]
-theorem infₛ_toSubalgebra (S : Set (StarSubalgebra R A)) :
-    (infₛ S).toSubalgebra = infₛ (StarSubalgebra.toSubalgebra '' S) :=
+theorem sInf_toSubalgebra (S : Set (StarSubalgebra R A)) :
+    (sInf S).toSubalgebra = sInf (StarSubalgebra.toSubalgebra '' S) :=
   SetLike.coe_injective <| by simp
-#align star_subalgebra.Inf_to_subalgebra StarSubalgebra.infₛ_toSubalgebra
+#align star_subalgebra.Inf_to_subalgebra StarSubalgebra.sInf_toSubalgebra
 
-/- warning: star_subalgebra.coe_infi -> StarSubalgebra.coe_infᵢ is a dubious translation:
+/- warning: star_subalgebra.coe_infi -> StarSubalgebra.coe_iInf 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)}, 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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (infᵢ.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (Set.interᵢ.{u2, u3} A ι (fun (i : ι) => (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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (S i)))
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)}, 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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (iInf.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (Set.iInter.{u2, u3} A ι (fun (i : ι) => (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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (S i)))
 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)}, Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (infᵢ.{u1, u3} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (Set.interᵢ.{u1, u3} A ι (fun (i : ι) => SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (S i)))
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_infi StarSubalgebra.coe_infᵢₓ'. -/
+  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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)}, Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (iInf.{u1, u3} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (Set.iInter.{u1, u3} A ι (fun (i : ι) => SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (S i)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_infi StarSubalgebra.coe_iInfₓ'. -/
 @[simp, norm_cast]
-theorem coe_infᵢ {ι : Sort _} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
-  simp [infᵢ]
-#align star_subalgebra.coe_infi StarSubalgebra.coe_infᵢ
+theorem coe_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
+  simp [iInf]
+#align star_subalgebra.coe_infi StarSubalgebra.coe_iInf
 
-/- warning: star_subalgebra.mem_infi -> StarSubalgebra.mem_infᵢ is a dubious translation:
+/- warning: star_subalgebra.mem_infi -> StarSubalgebra.mem_iInf 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (infᵢ.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (S i))
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (iInf.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (S i))
 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (infᵢ.{u1, u3} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (S i))
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_infi StarSubalgebra.mem_infᵢₓ'. -/
-theorem mem_infᵢ {ι : Sort _} {S : ι → StarSubalgebra R A} {x : A} :
-    (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [infᵢ, mem_Inf, Set.forall_range_iff]
-#align star_subalgebra.mem_infi StarSubalgebra.mem_infᵢ
+  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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (iInf.{u1, u3} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (S i))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_infi StarSubalgebra.mem_iInfₓ'. -/
+theorem mem_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} {x : A} :
+    (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [iInf, mem_Inf, Set.forall_range_iff]
+#align star_subalgebra.mem_infi StarSubalgebra.mem_iInf
 
-/- warning: star_subalgebra.infi_to_subalgebra -> StarSubalgebra.infᵢ_toSubalgebra is a dubious translation:
+/- warning: star_subalgebra.infi_to_subalgebra -> StarSubalgebra.iInf_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {ι : Sort.{u3}} (S : ι -> (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (infᵢ.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (infᵢ.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (S i)))
+  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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {ι : Sort.{u3}} (S : ι -> (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (iInf.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (iInf.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (S i)))
 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {ι : Sort.{u3}} (S : ι -> (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (infᵢ.{u1, u3} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (infᵢ.{u1, u3} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toInfSet.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (S i)))
-Case conversion may be inaccurate. Consider using '#align star_subalgebra.infi_to_subalgebra StarSubalgebra.infᵢ_toSubalgebraₓ'. -/
+  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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {ι : Sort.{u3}} (S : ι -> (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (iInf.{u1, u3} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (iInf.{u1, u3} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toInfSet.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (S i)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.infi_to_subalgebra StarSubalgebra.iInf_toSubalgebraₓ'. -/
 @[simp]
-theorem infᵢ_toSubalgebra {ι : Sort _} (S : ι → StarSubalgebra R A) :
+theorem iInf_toSubalgebra {ι : Sort _} (S : ι → StarSubalgebra R A) :
     (⨅ i, S i).toSubalgebra = ⨅ i, (S i).toSubalgebra :=
   SetLike.coe_injective <| by simp
-#align star_subalgebra.infi_to_subalgebra StarSubalgebra.infᵢ_toSubalgebra
+#align star_subalgebra.infi_to_subalgebra StarSubalgebra.iInf_toSubalgebra
 
 /- warning: star_subalgebra.bot_to_subalgebra -> StarSubalgebra.bot_toSubalgebra is a dubious translation:
 lean 3 declaration is

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

@@ -243,7 +243,7 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} ((fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) 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 but is expected to have type
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_inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A 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(AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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_inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
@@ -254,7 +254,7 @@ theorem coe_subtype : (S.Subtype : S → A) = coe :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S), Eq.{succ u2} A (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R 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(Semiring.toNonUnitalSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 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(AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))))) x)
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
@@ -294,7 +294,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 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(StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
@@ -339,7 +339,7 @@ theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u2, succ u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
@@ -372,7 +372,7 @@ theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => Exists.{0} (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (fun (H : Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) y)))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
@@ -394,7 +394,7 @@ theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -445,7 +445,7 @@ theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u3, succ u2} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
@@ -481,7 +481,7 @@ theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) S)
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -492,7 +492,7 @@ theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x 
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
@@ -1247,7 +1247,7 @@ def equalizer : StarSubalgebra R A
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.Mem.{u3, u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u4} B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f x) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g x))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
+  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
@@ -1258,7 +1258,7 @@ theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (LE.le.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
@@ -1268,7 +1268,7 @@ theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAl
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {s : Set.{u3} A}, (Eq.{succ u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (Eq.{succ u1} F f g))
 but is expected to have type
-  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
+  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
@@ -1280,7 +1280,7 @@ omit hF
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_8)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (s : Set.{u2} A), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) f) s))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
@@ -1292,7 +1292,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {s : Set.{u3} A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A 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x))) -> (Eq.{succ u1} F f g)
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
+  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
@@ -1312,7 +1312,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 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u3} A (Set.{u3} A) (Set.hasSingleton.{u3} A) a))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) _inst_10))) g (Subtype.mk.{succ u3} A (fun (x : A) => Membership.Mem.{u3, u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u3, u3} A (Set.{u3} A) (Set.hasSingleton.{u3} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u1} F f g)
 but is expected to have type
-  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) 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_inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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+  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) 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(Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3333 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) 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(StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 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x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) (FunLike.coe.{succ u4, succ u2, succ u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) 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_inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=

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

@@ -243,7 +243,7 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} ((fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (coeFn.{succ u2, 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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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
@@ -254,7 +254,7 @@ theorem coe_subtype : (S.Subtype : S → A) = coe :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S), Eq.{succ u2} A (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarAlgHom.hasCoeToFun.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))))) x)
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A 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(AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
@@ -294,7 +294,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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 but is expected to have type
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u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
@@ -339,7 +339,7 @@ theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u2, succ u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
@@ -372,7 +372,7 @@ theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => Exists.{0} (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (fun (H : Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) y)))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
@@ -394,7 +394,7 @@ theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -445,7 +445,7 @@ theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u3, succ u2} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
@@ -481,7 +481,7 @@ theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) S)
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -492,7 +492,7 @@ theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x 
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
@@ -1247,7 +1247,7 @@ def equalizer : StarSubalgebra R A
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.Mem.{u3, u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u4} B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f x) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g x))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
+  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
@@ -1258,7 +1258,7 @@ theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (LE.le.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
@@ -1268,7 +1268,7 @@ theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAl
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {s : Set.{u3} A}, (Eq.{succ u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (Eq.{succ u1} F f g))
 but is expected to have type
-  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
+  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
@@ -1280,7 +1280,7 @@ omit hF
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_8)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (s : Set.{u2} A), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) f) s))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
@@ -1292,7 +1292,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {s : Set.{u3} A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A 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_inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)), (Membership.Mem.{u3, u3} A (Set.{u3} A) (Set.hasMem.{u3} A) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 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 but is expected to have type
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_inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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+  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} 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_inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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_inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
@@ -1312,7 +1312,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 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 but is expected to have type
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(StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) 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_inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
+  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) 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(Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) (FunLike.coe.{succ u4, succ u2, succ u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3327 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=

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

@@ -243,7 +243,7 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} ((fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarAlgHom.hasCoeToFun.{u1, u2, u2} R (coeSort.{succ u2, 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(NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))))))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A 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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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_inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
@@ -254,7 +254,7 @@ theorem coe_subtype : (S.Subtype : S → A) = coe :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S), Eq.{succ u2} A (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R 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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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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_inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
@@ -294,7 +294,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) -> (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂)) (StarAlgHom.hasCoeToFun.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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(StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
@@ -339,7 +339,7 @@ theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u2, succ u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
@@ -372,7 +372,7 @@ theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => Exists.{0} (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (fun (H : Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) y)))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
@@ -394,7 +394,7 @@ theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -445,7 +445,7 @@ theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u3, succ u2} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
@@ -481,7 +481,7 @@ theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) S)
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -492,7 +492,7 @@ theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x 
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
@@ -1247,7 +1247,7 @@ def equalizer : StarSubalgebra R A
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.Mem.{u3, u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u4} B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f x) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g x))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
+  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
@@ -1258,7 +1258,7 @@ theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (LE.le.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
@@ -1268,7 +1268,7 @@ theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAl
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {s : Set.{u3} A}, (Eq.{succ u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (Eq.{succ u1} F f g))
 but is expected to have type
-  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
+  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
@@ -1280,7 +1280,7 @@ omit hF
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_8)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (s : Set.{u2} A), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) f) s))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
@@ -1292,7 +1292,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {s : Set.{u3} A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A 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x))) -> (Eq.{succ u1} F f g)
 but is expected to have type
-  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
+  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
@@ -1312,7 +1312,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 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_inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u1} F f g)
 but is expected to have type
-  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) 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_inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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+  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) 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(Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) 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(StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 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x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) (FunLike.coe.{succ u4, succ u2, succ u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3329 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A 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_inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f

@@ -243,7 +243,7 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} ((fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (coeFn.{succ u2, 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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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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(StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A 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(AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
@@ -254,7 +254,7 @@ theorem coe_subtype : (S.Subtype : S → A) = coe :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S), Eq.{succ u2} A (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarAlgHom.hasCoeToFun.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))))) x)
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A 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(AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
@@ -294,7 +294,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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 but is expected to have type
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u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
@@ -339,7 +339,7 @@ theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u2, succ u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
@@ -372,7 +372,7 @@ theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => Exists.{0} (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (fun (H : Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) y)))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
@@ -394,7 +394,7 @@ theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -445,7 +445,7 @@ theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u3, succ u2} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
@@ -481,7 +481,7 @@ theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) S)
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -492,7 +492,7 @@ theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x 
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
@@ -1247,7 +1247,7 @@ def equalizer : StarSubalgebra R A
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.Mem.{u3, u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u4} B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f x) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g x))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
+  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
@@ -1258,7 +1258,7 @@ theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (LE.le.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
@@ -1268,7 +1268,7 @@ theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAl
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {s : Set.{u3} A}, (Eq.{succ u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (Eq.{succ u1} F f g))
 but is expected to have type
-  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
+  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
@@ -1280,7 +1280,7 @@ omit hF
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_8)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (s : Set.{u2} A), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) f) s))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
@@ -1292,7 +1292,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {s : Set.{u3} A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A 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_inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)), (Membership.Mem.{u3, u3} A (Set.{u3} A) (Set.hasMem.{u3} A) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 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 but is expected to have type
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(SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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_inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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+  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} 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_inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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_inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
@@ -1312,7 +1312,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 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 but is expected to have type
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(StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) 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_inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
+  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) (FunLike.coe.{succ u4, succ u2, succ u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) (FunLike.coe.{succ u4, succ u2, succ u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3050 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

@@ -243,7 +243,7 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} ((fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarAlgHom.hasCoeToFun.{u1, u2, u2} R (coeSort.{succ u2, 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(NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))))))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} 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_inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A 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_inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => 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_inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
@@ -254,7 +254,7 @@ theorem coe_subtype : (S.Subtype : S → A) = coe :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S), Eq.{succ u2} A (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R 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 but is expected to have type
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(StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A 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(StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
@@ -264,7 +264,7 @@ theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (AlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_5)) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_3 (Subalgebra.algebra.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_5) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarAlgHom.toAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5)) x (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_5) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarAlgHom.toAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (AlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5)) x (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_3 (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) _inst_5) (Subalgebra.val.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarAlgHom.toAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.to_subalgebra_subtype StarSubalgebra.toSubalgebra_subtypeₓ'. -/
 @[simp]
 theorem toSubalgebra_subtype : S.toSubalgebra.val = S.Subtype.toAlgHom :=
@@ -275,7 +275,7 @@ theorem toSubalgebra_subtype : S.toSubalgebra.val = S.Subtype.toAlgHom :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂))
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂))
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion StarSubalgebra.inclusionₓ'. -/
 /-- The inclusion map between `star_subalgebra`s given by `subtype.map id` as a `star_alg_hom`. -/
 @[simps]
@@ -294,7 +294,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 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(StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
@@ -305,7 +305,7 @@ theorem inclusion_injective {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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Eq.{succ u2} (StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (StarAlgHom.comp.{u1, u2, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarSubalgebra.inclusion.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h)) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)
 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Eq.{succ 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) A _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.instStarSubtypeMemInstMembership.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4)))) (StarAlgHom.comp.{u2, u1, 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) A _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.instStarSubtypeMemInstMembership.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.instStarSubtypeMemInstMembership.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h)) (StarSubalgebra.subtype.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)
+  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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Eq.{succ 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) A _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4)))) (StarAlgHom.comp.{u2, u1, 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) A _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.star.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h)) (StarSubalgebra.subtype.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_comp_inclusion StarSubalgebra.subtype_comp_inclusionₓ'. -/
 @[simp]
 theorem subtype_comp_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
@@ -872,7 +872,7 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {s : Set.{u2} A} {p : (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> Prop} (a : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)), (forall (x : A) (h : Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s), p (Subtype.mk.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A 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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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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 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_inst_5 _inst_6 s))), (p x) -> (p (Star.star.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 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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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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 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_inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)))))))) (algebraMap.{u1, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) r)) -> (forall (x : Subtype.{succ u2} A (fun (x : A) => 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_inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (instHAdd.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Distrib.toAdd.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subsemiring.toNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)))))))) x y))) -> (forall (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (y : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (p x) -> (p y) -> (p (HMul.hMul.{u2, u2, u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 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_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (Submonoid.mul.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Subsemiring.toSubmonoid.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)))))) x y))) -> (forall (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (p x) -> (p (Star.star.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarMemClass.star.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) x))) -> (p a)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction' StarSubalgebra.adjoin_induction'ₓ'. -/
 /-- The difference with `star_subalgebra.adjoin_induction` is that this acts on the subtype. -/
 theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
@@ -1292,7 +1292,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {s : Set.{u3} A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) B _inst_1 (SubsemiringClass.toSemiring.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) A _inst_3 (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.subsemiringClass.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.algebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.hasStar.{u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 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 but is expected to have type
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(AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) 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_inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
+  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.star.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
@@ -1312,7 +1312,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 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_inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u1} F f g)
 but is expected to have type
-  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a))) 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_inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
+  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) 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_inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.star.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=

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

@@ -243,7 +243,7 @@ def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) }
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} ((fun (_x : StarAlgHom.{u1, u2, u2} R (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) A _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) => (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S) -> A) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (coeFn.{succ u2, 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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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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(StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A 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_inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (forall (a : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) a) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
 theorem coe_subtype : (S.Subtype : S → A) = coe :=
@@ -254,7 +254,7 @@ theorem coe_subtype : (S.Subtype : S → A) = coe :=
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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 but is expected to have type
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(StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) (fun (_x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) _x) (StarHomClass.toFunLike.{u2, u2, u2} (StarAlgHom.{u1, u2, u2} 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_inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
+  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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A 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(StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
@@ -294,7 +294,7 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Function.Injective.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) (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_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₁) (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S₂) _inst_1 (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.subsemiringClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.hasStar.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (SubsemiringClass.toSemiring.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂ A _inst_3 (StarSubalgebra.setLike.{u1, u2} R A _inst_1 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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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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 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_inst_6) S₂)) R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) 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_inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
@@ -339,7 +339,7 @@ theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u2, succ u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
@@ -372,7 +372,7 @@ theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => Exists.{0} (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (fun (H : Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) y)))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.mem.{u1, u1} B (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => And (Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) x) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (a : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) a) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
@@ -394,7 +394,7 @@ theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} B) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
@@ -445,7 +445,7 @@ theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f)) -> (Function.Injective.{succ u3, succ u2} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
@@ -481,7 +481,7 @@ theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) S)
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
@@ -492,7 +492,7 @@ theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x 
 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
 Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
@@ -1247,7 +1247,7 @@ def equalizer : StarSubalgebra R A
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.Mem.{u3, u3} A (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u4} B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f x) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g x))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
+  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [hF : StarAlgHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] (f : F) (g : F) (x : A), Iff (Membership.mem.{u4, u4} A (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarAlgHom.equalizer.{u2, u3, u4, u1} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) f x) (FunLike.coe.{succ u2, succ u4, succ u1} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u1} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u3, u4, u1} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
@@ -1258,7 +1258,7 @@ theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (LE.le.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteSemilatticeInf.toPartialOrder.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toCompleteSemilatticeInf.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 but is expected to have type
-  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
@@ -1268,7 +1268,7 @@ theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAl
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {s : Set.{u3} A}, (Eq.{succ u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (Eq.{succ u1} F f g))
 but is expected to have type
-  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
+  forall {F : Type.{u1}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [hF : StarAlgHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) f) (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u3, u4, u2} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
@@ -1280,7 +1280,7 @@ omit hF
 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_8)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (s : Set.{u2} A), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) f) s))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
@@ -1292,7 +1292,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {s : Set.{u3} A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A 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_inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)), (Membership.Mem.{u3, u3} A (Set.{u3} A) (Set.hasMem.{u3} A) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u3} (SetLike.hasCoeToSort.{u3, u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 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 but is expected to have type
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(InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
+  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => 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_inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A 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(Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3024 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A 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g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
@@ -1312,7 +1312,7 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
 lean 3 declaration is
   forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 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 but is expected to have type
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_inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) 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_inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
+  forall {F : Type.{u4}} {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A 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_inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
 Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Jireh Loreaux
 
 ! This file was ported from Lean 3 source module algebra.star.subalgebra
-! leanprover-community/mathlib commit 160ef3e338a2a4f21a280e4c152d4016156e516d
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.RingTheory.Adjoin.Basic
 /-!
 # Star subalgebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A *-subalgebra is a subalgebra of a *-algebra which is closed under *.
 
 The centralizer of a *-closed set is a *-subalgebra.

mathlib commit https://github.com/leanprover-community/mathlib/commit/f24cc2891c0e328f0ee8c57387103aa462c44b5e

@@ -25,11 +25,13 @@ The centralizer of a *-closed set is a *-subalgebra.
 
 universe u v
 
+#print StarSubalgebra /-
 /-- A *-subalgebra is a subalgebra of a *-algebra which is closed under *. -/
 structure StarSubalgebra (R : Type u) (A : Type v) [CommSemiring R] [StarRing R] [Semiring A]
   [StarRing A] [Algebra R A] [StarModule R A] extends Subalgebra R A : Type v where
   star_mem' {a} : a ∈ carrier → star a ∈ carrier
 #align star_subalgebra StarSubalgebra
+-/
 
 namespace StarSubalgebra
 
@@ -75,40 +77,79 @@ instance (s : StarSubalgebra R A) : Algebra R s :=
 instance (s : StarSubalgebra R A) : StarModule R s
     where star_smul r a := Subtype.ext (star_smul r a)
 
+/- warning: star_subalgebra.mem_carrier -> StarSubalgebra.mem_carrier 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {x : A}, Iff (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x (StarSubalgebra.carrier.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {s : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {x : A}, Iff (Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (Subsemigroup.carrier.{u1} A (MulOneClass.toMul.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3)))) (Submonoid.toSubsemigroup.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (NonAssocSemiring.toMulZeroOneClass.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3))) (Subsemiring.toSubmonoid.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3) (Subalgebra.toSubsemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)))))) (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x s)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_carrier StarSubalgebra.mem_carrierₓ'. -/
 @[simp]
 theorem mem_carrier {s : StarSubalgebra R A} {x : A} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align star_subalgebra.mem_carrier StarSubalgebra.mem_carrier
 
+/- warning: star_subalgebra.ext -> StarSubalgebra.ext 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {T : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, (forall (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x T)) -> (Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {T : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, (forall (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x T)) -> (Eq.{succ u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S T)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.ext StarSubalgebra.extₓ'. -/
 @[ext]
 theorem ext {S T : StarSubalgebra R A} (h : ∀ x : A, x ∈ S ↔ x ∈ T) : S = T :=
   SetLike.ext h
 #align star_subalgebra.ext StarSubalgebra.ext
 
+/- warning: star_subalgebra.mem_to_subalgebra -> StarSubalgebra.mem_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {x : A}, Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_5)) x (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {x : A}, Iff (Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5)) x (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_to_subalgebra StarSubalgebra.mem_toSubalgebraₓ'. -/
 @[simp]
 theorem mem_toSubalgebra {S : StarSubalgebra R A} {x} : x ∈ S.toSubalgebra ↔ x ∈ S :=
   Iff.rfl
 #align star_subalgebra.mem_to_subalgebra StarSubalgebra.mem_toSubalgebra
 
+/- warning: star_subalgebra.coe_to_subalgebra -> StarSubalgebra.coe_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_5)))) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_to_subalgebra StarSubalgebra.coe_toSubalgebraₓ'. -/
 @[simp]
 theorem coe_toSubalgebra (S : StarSubalgebra R A) : (S.toSubalgebra : Set A) = S :=
   rfl
 #align star_subalgebra.coe_to_subalgebra StarSubalgebra.coe_toSubalgebra
 
+#print StarSubalgebra.toSubalgebra_injective /-
 theorem toSubalgebra_injective :
     Function.Injective (toSubalgebra : StarSubalgebra R A → Subalgebra R A) := fun S T h =>
   ext fun x => by rw [← mem_to_subalgebra, ← mem_to_subalgebra, h]
 #align star_subalgebra.to_subalgebra_injective StarSubalgebra.toSubalgebra_injective
+-/
 
+/- warning: star_subalgebra.to_subalgebra_inj -> StarSubalgebra.toSubalgebra_inj 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {U : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, Iff (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 U)) (Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S U)
+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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {U : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, Iff (Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 U)) (Eq.{succ u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S U)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.to_subalgebra_inj StarSubalgebra.toSubalgebra_injₓ'. -/
 theorem toSubalgebra_inj {S U : StarSubalgebra R A} : S.toSubalgebra = U.toSubalgebra ↔ S = U :=
   toSubalgebra_injective.eq_iff
 #align star_subalgebra.to_subalgebra_inj StarSubalgebra.toSubalgebra_inj
 
+/- warning: star_subalgebra.to_subalgebra_le_iff -> StarSubalgebra.toSubalgebra_le_iff 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, Iff (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_5) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_5))))) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂)
+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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, Iff (LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_5))))) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.to_subalgebra_le_iff StarSubalgebra.toSubalgebra_le_iffₓ'. -/
 theorem toSubalgebra_le_iff {S₁ S₂ : StarSubalgebra R A} :
     S₁.toSubalgebra ≤ S₂.toSubalgebra ↔ S₁ ≤ S₂ :=
   Iff.rfl
 #align star_subalgebra.to_subalgebra_le_iff StarSubalgebra.toSubalgebra_le_iff
 
+#print StarSubalgebra.copy /-
 /-- Copy of a star subalgebra with a new `carrier` equal to the old one. Useful to fix definitional
 equalities. -/
 protected def copy (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : StarSubalgebra R A
@@ -119,55 +160,120 @@ protected def copy (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : StarSu
   algebraMap_mem' := hs.symm ▸ S.algebraMap_mem'
   star_mem' _ := hs.symm ▸ S.star_mem'
 #align star_subalgebra.copy StarSubalgebra.copy
+-/
 
+/- warning: star_subalgebra.coe_copy -> StarSubalgebra.coe_copy 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (s : Set.{u2} A) (hs : Eq.{succ u2} (Set.{u2} A) s ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S)), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.copy.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S s hs)) 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (s : Set.{u1} A) (hs : Eq.{succ u1} (Set.{u1} A) s (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.copy.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S s hs)) s
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_copy StarSubalgebra.coe_copyₓ'. -/
 @[simp]
 theorem coe_copy (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : (S.copy s hs : Set A) = s :=
   rfl
 #align star_subalgebra.coe_copy StarSubalgebra.coe_copy
 
+/- warning: star_subalgebra.copy_eq -> StarSubalgebra.copy_eq 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (s : Set.{u2} A) (hs : Eq.{succ u2} (Set.{u2} A) s ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S)), Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.copy.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S s hs) 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (s : Set.{u1} A) (hs : Eq.{succ u1} (Set.{u1} A) s (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)), Eq.{succ u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.copy.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S s hs) S
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.copy_eq StarSubalgebra.copy_eqₓ'. -/
 theorem copy_eq (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : S.copy s hs = S :=
   SetLike.coe_injective hs
 #align star_subalgebra.copy_eq StarSubalgebra.copy_eq
 
 variable (S : StarSubalgebra R A)
 
+/- warning: star_subalgebra.algebra_map_mem -> StarSubalgebra.algebraMap_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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (r : R), Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5) r) S
+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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5) r) S
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.algebra_map_mem StarSubalgebra.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ S :=
   S.algebraMap_mem' r
 #align star_subalgebra.algebra_map_mem StarSubalgebra.algebraMap_mem
 
+/- warning: star_subalgebra.srange_le -> StarSubalgebra.rangeS_le 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), LE.le.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Preorder.toLE.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (PartialOrder.toPreorder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Subsemiring.completeLattice.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (RingHom.rangeS.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
+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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), LE.le.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Preorder.toLE.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (PartialOrder.toPreorder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Subsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (Subsemiring.instCompleteLatticeSubsemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))) (RingHom.rangeS.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5)) (Subalgebra.toSubsemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.srange_le StarSubalgebra.rangeS_leₓ'. -/
 theorem rangeS_le : (algebraMap R A).srange ≤ S.toSubalgebra.toSubsemiring := fun x ⟨r, hr⟩ =>
   hr ▸ S.algebraMap_mem r
 #align star_subalgebra.srange_le StarSubalgebra.rangeS_le
 
+/- warning: star_subalgebra.range_subset -> StarSubalgebra.range_subset 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5))) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S)
+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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_5))) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.range_subset StarSubalgebra.range_subsetₓ'. -/
 theorem range_subset : Set.range (algebraMap R A) ⊆ S := fun x ⟨r, hr⟩ => hr ▸ S.algebraMap_mem r
 #align star_subalgebra.range_subset StarSubalgebra.range_subset
 
+/- warning: star_subalgebra.range_le -> StarSubalgebra.range_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align star_subalgebra.range_le StarSubalgebra.range_leₓ'. -/
 theorem range_le : Set.range (algebraMap R A) ≤ S :=
   S.range_subset
 #align star_subalgebra.range_le StarSubalgebra.range_le
 
+#print StarSubalgebra.smul_mem /-
 protected theorem smul_mem {x : A} (hx : x ∈ S) (r : R) : r • x ∈ S :=
   (Algebra.smul_def r x).symm ▸ mul_mem (S.algebraMap_mem r) hx
 #align star_subalgebra.smul_mem StarSubalgebra.smul_mem
+-/
 
+#print StarSubalgebra.subtype /-
 /-- Embedding of a subalgebra into the algebra. -/
 def subtype : S →⋆ₐ[R] A := by refine_struct { toFun := (coe : S → A) } <;> intros <;> rfl
 #align star_subalgebra.subtype StarSubalgebra.subtype
+-/
 
+/- warning: star_subalgebra.coe_subtype -> StarSubalgebra.coe_subtype is a dubious translation:
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+but is expected to have type
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_inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtypeₓ'. -/
 @[simp]
-theorem coeSubtype : (S.Subtype : S → A) = coe :=
+theorem coe_subtype : (S.Subtype : S → A) = coe :=
   rfl
-#align star_subalgebra.coe_subtype StarSubalgebra.coeSubtype
-
+#align star_subalgebra.coe_subtype StarSubalgebra.coe_subtype
+
+/- warning: star_subalgebra.subtype_apply -> StarSubalgebra.subtype_apply 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (x : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) => A) x) (FunLike.coe.{succ u2, succ u2, succ u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A 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(StarAlgHomClass.toStarHomClass.{u2, u1, u2, u2} (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A 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_inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S)) A _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))))) (StarSubalgebra.subtype.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) x) (Subtype.val.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S)) x)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_apply StarSubalgebra.subtype_applyₓ'. -/
 theorem subtype_apply (x : S) : S.Subtype x = (x : A) :=
   rfl
 #align star_subalgebra.subtype_apply StarSubalgebra.subtype_apply
 
+/- warning: star_subalgebra.to_subalgebra_subtype -> StarSubalgebra.toSubalgebra_subtype 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align star_subalgebra.to_subalgebra_subtype StarSubalgebra.toSubalgebra_subtypeₓ'. -/
 @[simp]
 theorem toSubalgebra_subtype : S.toSubalgebra.val = S.Subtype.toAlgHom :=
   rfl
 #align star_subalgebra.to_subalgebra_subtype StarSubalgebra.toSubalgebra_subtype
 
+/- warning: star_subalgebra.inclusion -> StarSubalgebra.inclusion 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (StarAlgHom.{u1, u2, u2} R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion StarSubalgebra.inclusionₓ'. -/
 /-- The inclusion map between `star_subalgebra`s given by `subtype.map id` as a `star_alg_hom`. -/
 @[simps]
 def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆ₐ[R] S₂
@@ -181,11 +287,23 @@ def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆
   map_star' x := rfl
 #align star_subalgebra.inclusion StarSubalgebra.inclusion
 
+/- warning: star_subalgebra.inclusion_injective -> StarSubalgebra.inclusion_injective is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂)))) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injectiveₓ'. -/
 theorem inclusion_injective {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     Function.Injective <| inclusion h :=
   Set.inclusion_injective h
 #align star_subalgebra.inclusion_injective StarSubalgebra.inclusion_injective
 
+/- warning: star_subalgebra.subtype_comp_inclusion -> StarSubalgebra.subtype_comp_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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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 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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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] {S₁ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} (h : LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂), Eq.{succ 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) A _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.instStarSubtypeMemInstMembership.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4)))) (StarAlgHom.comp.{u2, u1, 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_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₁)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S₂)) A _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) (StarMemClass.instStarSubtypeMemInstMembership.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₁) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 _inst_3 _inst_5 (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂)) (StarSubalgebra.algebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarMemClass.instStarSubtypeMemInstMembership.{u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.starMemClass.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S₂) _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (StarSubalgebra.subtype.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₂) (StarSubalgebra.inclusion.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁ S₂ h)) (StarSubalgebra.subtype.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.subtype_comp_inclusion StarSubalgebra.subtype_comp_inclusionₓ'. -/
 @[simp]
 theorem subtype_comp_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) :
     S₂.Subtype.comp (inclusion h) = S₁.Subtype :=
@@ -194,6 +312,7 @@ theorem subtype_comp_inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S
 
 section Map
 
+#print StarSubalgebra.map /-
 /-- Transport a star subalgebra via a star algebra homomorphism. -/
 def map (f : A →⋆ₐ[R] B) (S : StarSubalgebra R A) : StarSubalgebra R B :=
   { S.toSubalgebra.map f.toAlgHom with
@@ -201,61 +320,130 @@ def map (f : A →⋆ₐ[R] B) (S : StarSubalgebra R A) : StarSubalgebra R B :=
       rintro _ ⟨a, ha, rfl⟩
       exact map_star f a ▸ Set.mem_image_of_mem _ (S.star_mem' ha) }
 #align star_subalgebra.map StarSubalgebra.map
+-/
 
+/- warning: star_subalgebra.map_mono -> StarSubalgebra.map_mono 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S₁ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S₁ : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {S₂ : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (LE.le.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S₁ S₂) -> (LE.le.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_mono StarSubalgebra.map_monoₓ'. -/
 theorem map_mono {S₁ S₂ : StarSubalgebra R A} {f : A →⋆ₐ[R] B} : S₁ ≤ S₂ → S₁.map f ≤ S₂.map f :=
   Set.image_subset f
 #align star_subalgebra.map_mono StarSubalgebra.map_mono
 
+/- warning: star_subalgebra.map_injective -> StarSubalgebra.map_injective 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B 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(StarAddMonoid.toHasInvolutiveStar.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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
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(AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u2, succ u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_injective StarSubalgebra.map_injectiveₓ'. -/
 theorem map_injective {f : A →⋆ₐ[R] B} (hf : Function.Injective f) : Function.Injective (map f) :=
   fun S₁ S₂ ih =>
   ext <| Set.ext_iff.1 <| Set.image_injective.2 hf <| Set.ext <| SetLike.ext_iff.mp ih
 #align star_subalgebra.map_injective StarSubalgebra.map_injective
 
+/- warning: star_subalgebra.map_id -> StarSubalgebra.map_id 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.map.{u1, u2, u2} R A A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_3 _inst_4 _inst_5 _inst_6 (StarAlgHom.id.{u1, u2} R A _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) S) 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.map.{u2, u1, u1} R A A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_3 _inst_4 _inst_5 _inst_6 (StarAlgHom.id.{u2, u1} R A _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4)))) S) S
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_id StarSubalgebra.map_idₓ'. -/
 @[simp]
 theorem map_id (S : StarSubalgebra R A) : S.map (StarAlgHom.id R A) = S :=
   SetLike.coe_injective <| Set.image_id _
 #align star_subalgebra.map_id StarSubalgebra.map_id
 
+/- warning: star_subalgebra.map_map -> StarSubalgebra.map_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] [_inst_11 : Semiring.{u4} C] [_inst_12 : StarRing.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)] [_inst_13 : Algebra.{u1, u4} R C _inst_1 _inst_11] [_inst_14 : StarModule.{u1, u4} R C (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.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12))) (SMulZeroClass.toHasSmul.{u1, u4} R C (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R C (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R C (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (Module.toMulActionWithZero.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_11 _inst_13)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (g : StarAlgHom.{u1, u3, u4} R B C _inst_1 _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toHasStar.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12)))) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u4} (StarSubalgebra.{u1, u4} R C _inst_1 _inst_2 _inst_11 _inst_12 _inst_13 _inst_14) (StarSubalgebra.map.{u1, u3, u4} R B C _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 g (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (StarSubalgebra.map.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_11 _inst_12 _inst_13 _inst_14 (StarAlgHom.comp.{u1, u2, u3, u4} R A B C _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toHasStar.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12))) g f) S)
+but is expected to have type
+  forall {R : Type.{u4}} {A : Type.{u3}} {B : Type.{u2}} {C : Type.{u1}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : StarRing.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1))] [_inst_3 : Semiring.{u3} A] [_inst_4 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_5 : Algebra.{u4, u3} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u4, u3} R A (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u3} A (StarAddMonoid.toInvolutiveStar.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_4))) (Algebra.toSMul.{u4, u3} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u4, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u4, u2} R B (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u4, u2} R B _inst_1 _inst_7 _inst_9)] [_inst_11 : Semiring.{u1} C] [_inst_12 : StarRing.{u1} C (Semiring.toNonUnitalSemiring.{u1} C _inst_11)] [_inst_13 : Algebra.{u4, u1} R C _inst_1 _inst_11] [_inst_14 : StarModule.{u4, u1} R C (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} C (StarAddMonoid.toInvolutiveStar.{u1} C (AddMonoidWithOne.toAddMonoid.{u1} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} C (NonAssocSemiring.toAddCommMonoidWithOne.{u1} C (Semiring.toNonAssocSemiring.{u1} C _inst_11)))) (StarRing.toStarAddMonoid.{u1} C (Semiring.toNonUnitalSemiring.{u1} C _inst_11) _inst_12))) (Algebra.toSMul.{u4, u1} R C _inst_1 _inst_11 _inst_13)] (S : StarSubalgebra.{u4, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (g : StarAlgHom.{u4, u2, u1} R B C _inst_1 _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toStar.{u1} C (StarAddMonoid.toInvolutiveStar.{u1} C (AddMonoidWithOne.toAddMonoid.{u1} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} C (NonAssocSemiring.toAddCommMonoidWithOne.{u1} C (Semiring.toNonAssocSemiring.{u1} C _inst_11)))) (StarRing.toStarAddMonoid.{u1} C (Semiring.toNonUnitalSemiring.{u1} C _inst_11) _inst_12)))) (f : StarAlgHom.{u4, u3, u2} R A B _inst_1 _inst_3 _inst_5 (InvolutiveStar.toStar.{u3} A (StarAddMonoid.toInvolutiveStar.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (StarSubalgebra.{u4, u1} R C _inst_1 _inst_2 _inst_11 _inst_12 _inst_13 _inst_14) (StarSubalgebra.map.{u4, u2, u1} R B C _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 g (StarSubalgebra.map.{u4, u3, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (StarSubalgebra.map.{u4, u3, u1} R A C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_11 _inst_12 _inst_13 _inst_14 (StarAlgHom.comp.{u4, u3, u2, u1} R A B C _inst_1 _inst_3 _inst_5 (InvolutiveStar.toStar.{u3} A (StarAddMonoid.toInvolutiveStar.{u3} A (AddMonoidWithOne.toAddMonoid.{u3} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} A (NonAssocSemiring.toAddCommMonoidWithOne.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toStar.{u1} C (StarAddMonoid.toInvolutiveStar.{u1} C (AddMonoidWithOne.toAddMonoid.{u1} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} C (NonAssocSemiring.toAddCommMonoidWithOne.{u1} C (Semiring.toNonAssocSemiring.{u1} C _inst_11)))) (StarRing.toStarAddMonoid.{u1} C (Semiring.toNonUnitalSemiring.{u1} C _inst_11) _inst_12))) g f) S)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_map StarSubalgebra.map_mapₓ'. -/
 theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ[R] B) :
     (S.map f).map g = S.map (g.comp f) :=
   SetLike.coe_injective <| Set.image_image _ _ _
 #align star_subalgebra.map_map StarSubalgebra.map_map
 
+/- warning: star_subalgebra.mem_map -> StarSubalgebra.mem_map 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {y : B}, Iff (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) y (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Exists.{succ u2} A (fun (x : A) => Exists.{0} (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) (fun (H : Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x S) => Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) y)))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A 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_inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f x) y)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_map StarSubalgebra.mem_mapₓ'. -/
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map
 #align star_subalgebra.mem_map StarSubalgebra.mem_map
 
+/- warning: star_subalgebra.map_to_subalgebra -> StarSubalgebra.map_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, Eq.{succ u3} (Subalgebra.{u1, u3} R B _inst_1 _inst_7 _inst_9) (StarSubalgebra.toSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Subalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 _inst_7 _inst_9 (StarAlgHom.toAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) f) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, Eq.{succ u1} (Subalgebra.{u3, u1} R B _inst_1 _inst_7 _inst_9) (StarSubalgebra.toSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Subalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 _inst_7 _inst_9 (StarAlgHom.toAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) f) (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_to_subalgebra StarSubalgebra.map_toSubalgebraₓ'. -/
 theorem map_toSubalgebra {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} :
     (S.map f).toSubalgebra = S.toSubalgebra.map f.toAlgHom :=
   SetLike.coe_injective rfl
 #align star_subalgebra.map_to_subalgebra StarSubalgebra.map_toSubalgebra
 
+/- warning: star_subalgebra.coe_map -> StarSubalgebra.coe_map 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u3} (Set.{u3} B) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 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_inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A 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(AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B 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(InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B 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R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) S))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_map StarSubalgebra.coe_mapₓ'. -/
 @[simp]
 theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set B) = f '' S :=
   rfl
 #align star_subalgebra.coe_map StarSubalgebra.coe_map
 
+#print StarSubalgebra.comap /-
 /-- Preimage of a star subalgebra under an star algebra homomorphism. -/
 def comap (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) : StarSubalgebra R A :=
   { S.toSubalgebra.comap f.toAlgHom with
     star_mem' := fun a ha => show f (star a) ∈ S from (map_star f a).symm ▸ star_mem ha }
 #align star_subalgebra.comap StarSubalgebra.comap
+-/
 
+/- warning: star_subalgebra.map_le_iff_le_comap -> StarSubalgebra.map_le_iff_le_comap 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))} {U : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10}, Iff (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S) U) (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f U))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6} {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))} {U : StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10}, Iff (LE.le.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S) U) (LE.le.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f U))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_le_iff_le_comap StarSubalgebra.map_le_iff_le_comapₓ'. -/
 theorem map_le_iff_le_comap {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {U : StarSubalgebra R B} :
     map f S ≤ U ↔ S ≤ comap f U :=
   Set.image_subset_iff
 #align star_subalgebra.map_le_iff_le_comap StarSubalgebra.map_le_iff_le_comap
 
+/- warning: star_subalgebra.gc_map_comap -> StarSubalgebra.gc_map_comap 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), GaloisConnection.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f)
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))), GaloisConnection.{u2, u1} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10))) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.gc_map_comap StarSubalgebra.gc_map_comapₓ'. -/
 theorem gc_map_comap (f : A →⋆ₐ[R] B) : GaloisConnection (map f) (comap f) := fun S U =>
   map_le_iff_le_comap
 #align star_subalgebra.gc_map_comap StarSubalgebra.gc_map_comap
 
+/- warning: star_subalgebra.comap_mono -> StarSubalgebra.comap_mono 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] {S₁ : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {S₂ : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))}, (LE.le.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.partialOrder.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S₁ S₂) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] {S₁ : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {S₂ : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10} {f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))}, (LE.le.{u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Preorder.toLE.{u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S₁ S₂) -> (LE.le.{u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₁) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S₂))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_mono StarSubalgebra.comap_monoₓ'. -/
 theorem comap_mono {S₁ S₂ : StarSubalgebra R B} {f : A →⋆ₐ[R] B} :
     S₁ ≤ S₂ → S₁.comap f ≤ S₂.comap f :=
   Set.preimage_mono
 #align star_subalgebra.comap_mono StarSubalgebra.comap_mono
 
+/- warning: star_subalgebra.comap_injective -> StarSubalgebra.comap_injective 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B 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(Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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
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(NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u1} B] [_inst_8 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_9 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_9)] {f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))}, (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u2 u1, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u2 u1, u3, u2, u1} (StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_8)))))) f)) -> (Function.Injective.{succ u1, succ u2} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_injective StarSubalgebra.comap_injectiveₓ'. -/
 theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     Function.Injective (comap f) := fun S₁ S₂ h =>
   ext fun b =>
@@ -264,21 +452,45 @@ theorem comap_injective {f : A →⋆ₐ[R] B} (hf : Function.Surjective f) :
     hx ▸ this
 #align star_subalgebra.comap_injective StarSubalgebra.comap_injective
 
+/- warning: star_subalgebra.comap_id -> StarSubalgebra.comap_id 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u2} R A A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_3 _inst_4 _inst_5 _inst_6 (StarAlgHom.id.{u1, u2} R A _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4)))) S) 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 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_5)] (S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6), Eq.{succ u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u2, u1, u1} R A A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_3 _inst_4 _inst_5 _inst_6 (StarAlgHom.id.{u2, u1} R A _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4)))) S) S
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_id StarSubalgebra.comap_idₓ'. -/
 @[simp]
 theorem comap_id (S : StarSubalgebra R A) : S.comap (StarAlgHom.id R A) = S :=
   SetLike.coe_injective <| Set.preimage_id
 #align star_subalgebra.comap_id StarSubalgebra.comap_id
 
+/- warning: star_subalgebra.comap_comap -> StarSubalgebra.comap_comap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] [_inst_11 : Semiring.{u4} C] [_inst_12 : StarRing.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)] [_inst_13 : Algebra.{u1, u4} R C _inst_1 _inst_11] [_inst_14 : StarModule.{u1, u4} R C (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.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12))) (SMulZeroClass.toHasSmul.{u1, u4} R C (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} R C (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} R C (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} C (AddMonoid.toAddZeroClass.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11)))))) (Module.toMulActionWithZero.{u1, u4} R C (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonAssocSemiring.{u4} C _inst_11))) (Algebra.toModule.{u1, u4} R C _inst_1 _inst_11 _inst_13)))))] (S : StarSubalgebra.{u1, u4} R C _inst_1 _inst_2 _inst_11 _inst_12 _inst_13 _inst_14) (g : StarAlgHom.{u1, u3, u4} R B C _inst_1 _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toHasStar.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12)))) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f (StarSubalgebra.comap.{u1, u3, u4} R B C _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 g S)) (StarSubalgebra.comap.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_11 _inst_12 _inst_13 _inst_14 (StarAlgHom.comp.{u1, u2, u3, u4} R A B C _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toHasStar.{u4} C (StarAddMonoid.toHasInvolutiveStar.{u4} C (AddCommMonoid.toAddMonoid.{u4} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} C (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11)))) (StarRing.toStarAddMonoid.{u4} C (Semiring.toNonUnitalSemiring.{u4} C _inst_11) _inst_12))) g f) S)
+but is expected to have type
+  forall {R : Type.{u4}} {A : Type.{u1}} {B : Type.{u2}} {C : Type.{u3}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : StarRing.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u4, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u4, u1} R A (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u4, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u4, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u4, u2} R B (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u4, u2} R B _inst_1 _inst_7 _inst_9)] [_inst_11 : Semiring.{u3} C] [_inst_12 : StarRing.{u3} C (Semiring.toNonUnitalSemiring.{u3} C _inst_11)] [_inst_13 : Algebra.{u4, u3} R C _inst_1 _inst_11] [_inst_14 : StarModule.{u4, u3} R C (InvolutiveStar.toStar.{u4} R (StarAddMonoid.toInvolutiveStar.{u4} R (AddMonoidWithOne.toAddMonoid.{u4} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} R (NonAssocSemiring.toAddCommMonoidWithOne.{u4} R (Semiring.toNonAssocSemiring.{u4} R (CommSemiring.toSemiring.{u4} R _inst_1))))) (StarRing.toStarAddMonoid.{u4} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u4} R (CommSemiring.toNonUnitalCommSemiring.{u4} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u3} C (StarAddMonoid.toInvolutiveStar.{u3} C (AddMonoidWithOne.toAddMonoid.{u3} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} C (NonAssocSemiring.toAddCommMonoidWithOne.{u3} C (Semiring.toNonAssocSemiring.{u3} C _inst_11)))) (StarRing.toStarAddMonoid.{u3} C (Semiring.toNonUnitalSemiring.{u3} C _inst_11) _inst_12))) (Algebra.toSMul.{u4, u3} R C _inst_1 _inst_11 _inst_13)] (S : StarSubalgebra.{u4, u3} R C _inst_1 _inst_2 _inst_11 _inst_12 _inst_13 _inst_14) (g : StarAlgHom.{u4, u2, u3} R B C _inst_1 _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toStar.{u3} C (StarAddMonoid.toInvolutiveStar.{u3} C (AddMonoidWithOne.toAddMonoid.{u3} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} C (NonAssocSemiring.toAddCommMonoidWithOne.{u3} C (Semiring.toNonAssocSemiring.{u3} C _inst_11)))) (StarRing.toStarAddMonoid.{u3} C (Semiring.toNonUnitalSemiring.{u3} C _inst_11) _inst_12)))) (f : StarAlgHom.{u4, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (StarSubalgebra.{u4, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u4, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f (StarSubalgebra.comap.{u4, u2, u3} R B C _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 _inst_11 _inst_12 _inst_13 _inst_14 g S)) (StarSubalgebra.comap.{u4, u1, u3} R A C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_11 _inst_12 _inst_13 _inst_14 (StarAlgHom.comp.{u4, u1, u2, u3} R A B C _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) _inst_11 _inst_13 (InvolutiveStar.toStar.{u3} C (StarAddMonoid.toInvolutiveStar.{u3} C (AddMonoidWithOne.toAddMonoid.{u3} C (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} C (NonAssocSemiring.toAddCommMonoidWithOne.{u3} C (Semiring.toNonAssocSemiring.{u3} C _inst_11)))) (StarRing.toStarAddMonoid.{u3} C (Semiring.toNonUnitalSemiring.{u3} C _inst_11) _inst_12))) g f) S)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.comap_comap StarSubalgebra.comap_comapₓ'. -/
 theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ[R] B) :
     (S.comap g).comap f = S.comap (g.comp f) :=
   SetLike.coe_injective <| Set.preimage_preimage
 #align star_subalgebra.comap_comap StarSubalgebra.comap_comap
 
+/- warning: star_subalgebra.mem_comap -> StarSubalgebra.mem_comap 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B 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(StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (x : A), Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.Mem.{u3, u3} B (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.hasMem.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (InvolutiveStar.toHasStar.{u2} A 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(AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f x) S)
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A 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(Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) (x : A), Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) x (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) x) (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)) (FunLike.coe.{max (succ u1) (succ u2), succ 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(StarAddMonoid.toInvolutiveStar.{u1} A (AddMonoidWithOne.toAddMonoid.{u1} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} A (NonAssocSemiring.toAddCommMonoidWithOne.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) 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(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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f x) S)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_comap StarSubalgebra.mem_comapₓ'. -/
 @[simp]
 theorem mem_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) (x : A) : x ∈ S.comap f ↔ f x ∈ S :=
   Iff.rfl
 #align star_subalgebra.mem_comap StarSubalgebra.mem_comap
 
+/- warning: star_subalgebra.coe_comap -> StarSubalgebra.coe_comap 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_9 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_9)))))] (S : StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.comap.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) _inst_7 _inst_9 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_8)))) f) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (HasLiftT.mk.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (CoeTCₓ.coe.{succ u3, succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (Set.{u3} B) (SetLike.Set.hasCoeT.{u3, u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10)))) S))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_5 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_5)] [_inst_7 : Semiring.{u2} B] [_inst_8 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_9 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_9)] (S : StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.comap.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 _inst_10 f S)) (Set.preimage.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))) R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_5 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) _inst_7 _inst_9 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_8)))))) f) (SetLike.coe.{u2, u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) B (StarSubalgebra.setLike.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10) S))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_comap StarSubalgebra.coe_comapₓ'. -/
 @[simp, norm_cast]
 theorem coe_comap (S : StarSubalgebra R B) (f : A →⋆ₐ[R] B) :
     (S.comap f : Set A) = f ⁻¹' (S : Set B) :=
@@ -291,27 +503,53 @@ section Centralizer
 
 variable (R) {A}
 
+/- warning: set.star_mem_centralizer -> Set.star_mem_centralizer is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] {a : A} {s : Set.{u1} A}, (forall (a : A), (Membership.Mem.{u1, u1} A (Set.{u1} A) (Set.hasMem.{u1} A) a s) -> (Membership.Mem.{u1, u1} A (Set.{u1} A) (Set.hasMem.{u1} A) (Star.star.{u1} A (InvolutiveStar.toHasStar.{u1} A (StarAddMonoid.toHasInvolutiveStar.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) a) s)) -> (Membership.Mem.{u1, u1} A (Set.{u1} A) (Set.hasMem.{u1} A) a (Set.centralizer.{u1} A s (Distrib.toHasMul.{u1} A (NonUnitalNonAssocSemiring.toDistrib.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3)))))) -> (Membership.Mem.{u1, u1} A (Set.{u1} A) (Set.hasMem.{u1} A) (Star.star.{u1} A (InvolutiveStar.toHasStar.{u1} A (StarAddMonoid.toHasInvolutiveStar.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) a) (Set.centralizer.{u1} A s (Distrib.toHasMul.{u1} A (NonUnitalNonAssocSemiring.toDistrib.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3))))))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_3 : Semiring.{u1} A] [_inst_4 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] {a : A} {s : Set.{u1} A}, (forall (a : A), (Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) a s) -> (Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) (Star.star.{u1} A (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) a) s)) -> (Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) a (Set.centralizer.{u1} A s (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3))))) -> (Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) (Star.star.{u1} A (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_4))) a) (Set.centralizer.{u1} A s (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3)))))
+Case conversion may be inaccurate. Consider using '#align set.star_mem_centralizer Set.star_mem_centralizerₓ'. -/
 theorem Set.star_mem_centralizer {a : A} {s : Set A} (h : ∀ a : A, a ∈ s → star a ∈ s)
     (ha : a ∈ Set.centralizer s) : star a ∈ Set.centralizer s := fun y hy => by
   simpa using congr_arg star (ha _ (h _ hy)).symm
 #align set.star_mem_centralizer Set.star_mem_centralizer
 
+#print StarSubalgebra.centralizer /-
 /-- The centralizer, or commutant, of a *-closed set as star subalgebra. -/
 def centralizer (s : Set A) (w : ∀ a : A, a ∈ s → star a ∈ s) : StarSubalgebra R A :=
   { Subalgebra.centralizer R s with star_mem' := fun x => Set.star_mem_centralizer w }
 #align star_subalgebra.centralizer StarSubalgebra.centralizer
+-/
 
+/- warning: star_subalgebra.coe_centralizer -> StarSubalgebra.coe_centralizer 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (s : Set.{u2} A) (w : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)), 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_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s w)) (Set.centralizer.{u2} A s (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))))
+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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (s : Set.{u2} A) (w : forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s w)) (Set.centralizer.{u2} A s (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_centralizer StarSubalgebra.coe_centralizerₓ'. -/
 @[simp]
 theorem coe_centralizer (s : Set A) (w : ∀ a : A, a ∈ s → star a ∈ s) :
     (centralizer R s w : Set A) = s.centralizer :=
   rfl
 #align star_subalgebra.coe_centralizer StarSubalgebra.coe_centralizer
 
+/- warning: star_subalgebra.mem_centralizer_iff -> StarSubalgebra.mem_centralizer_iff 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] {s : Set.{u2} A} {w : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)} {z : A}, Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) z (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s w)) (forall (g : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) g s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) g z) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) z g)))
+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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] {s : Set.{u2} A} {w : forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)} {z : A}, Iff (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) z (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s w)) (forall (g : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) g s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) g z) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) z g)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_centralizer_iff StarSubalgebra.mem_centralizer_iffₓ'. -/
 theorem mem_centralizer_iff {s : Set A} {w} {z : A} :
     z ∈ centralizer R s w ↔ ∀ g ∈ s, g * z = z * g :=
   Iff.rfl
 #align star_subalgebra.mem_centralizer_iff StarSubalgebra.mem_centralizer_iff
 
+/- warning: star_subalgebra.centralizer_le -> StarSubalgebra.centralizer_le 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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_5)))))] (s : Set.{u2} A) (t : Set.{u2} A) (ws : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)) (wt : forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a t) -> (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) t)), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s t) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 t wt) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s ws))
+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 : Semiring.{u2} A] [_inst_4 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_5 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_5)] (s : Set.{u2} A) (t : Set.{u2} A) (ws : forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) s)) (wt : forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a t) -> (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_4))) a) t)), (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) s t) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 t wt) (StarSubalgebra.centralizer.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s ws))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.centralizer_le StarSubalgebra.centralizer_leₓ'. -/
 theorem centralizer_le (s t : Set A) (ws : ∀ a : A, a ∈ s → star a ∈ s)
     (wt : ∀ a : A, a ∈ t → star a ∈ t) (h : s ⊆ t) : centralizer R t wt ≤ centralizer R s ws :=
   Set.centralizer_subset h
@@ -356,26 +594,52 @@ instance : InvolutiveStar (Subalgebra R A)
     Subalgebra.ext fun x =>
       ⟨fun hx => star_star x ▸ hx, fun hx => ((star_star x).symm ▸ hx : star (star x) ∈ S)⟩
 
+/- warning: subalgebra.mem_star_iff -> Subalgebra.mem_star_iff 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (x : A), Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_4)) x (Star.star.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (InvolutiveStar.toHasStar.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Subalgebra.hasInvolutiveStar.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S)) (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_4)) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (x : A), Iff (Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4)) x (Star.star.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (InvolutiveStar.toStar.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Subalgebra.involutiveStar.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S)) (Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4)) (Star.star.{u1} A (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) x) S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.mem_star_iff Subalgebra.mem_star_iffₓ'. -/
 @[simp]
 theorem mem_star_iff (S : Subalgebra R A) (x : A) : x ∈ star S ↔ star x ∈ S :=
   Iff.rfl
 #align subalgebra.mem_star_iff Subalgebra.mem_star_iff
 
+/- warning: subalgebra.star_mem_star_iff -> Subalgebra.star_mem_star_iff 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (x : A), Iff (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_4)) (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x) (Star.star.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (InvolutiveStar.toHasStar.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Subalgebra.hasInvolutiveStar.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S)) (Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_4)) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (x : A), Iff (Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4)) (Star.star.{u1} A (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) x) (Star.star.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (InvolutiveStar.toStar.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Subalgebra.involutiveStar.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S)) (Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4)) x S)
+Case conversion may be inaccurate. Consider using '#align subalgebra.star_mem_star_iff Subalgebra.star_mem_star_iffₓ'. -/
 @[simp]
 theorem star_mem_star_iff (S : Subalgebra R A) (x : A) : star x ∈ star S ↔ x ∈ S := by
   simpa only [star_star] using mem_star_iff S (star x)
 #align subalgebra.star_mem_star_iff Subalgebra.star_mem_star_iff
 
+/- warning: subalgebra.coe_star -> Subalgebra.coe_star 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4), Eq.{succ u2} (Set.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_4)))) (Star.star.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (InvolutiveStar.toHasStar.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Subalgebra.hasInvolutiveStar.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S)) (Star.star.{u2} (Set.{u2} A) (Set.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_4)))) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Star.star.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (InvolutiveStar.toStar.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Subalgebra.involutiveStar.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) S)) (Star.star.{u1} (Set.{u1} A) (Set.star.{u1} A (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5)))) (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.coe_star Subalgebra.coe_starₓ'. -/
 @[simp]
 theorem coe_star (S : Subalgebra R A) : ((star S : Subalgebra R A) : Set A) = star S :=
   rfl
 #align subalgebra.coe_star Subalgebra.coe_star
 
+#print Subalgebra.star_mono /-
 theorem star_mono : Monotone (star : Subalgebra R A → Subalgebra R A) := fun _ _ h _ hx => h hx
 #align subalgebra.star_mono Subalgebra.star_mono
+-/
 
 variable (R)
 
+/- warning: subalgebra.star_adjoin_comm -> Subalgebra.star_adjoin_comm 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (s : Set.{u2} A), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Star.star.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (InvolutiveStar.toHasStar.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Subalgebra.hasInvolutiveStar.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (Algebra.adjoin.{u1, u2} R A _inst_1 _inst_3 _inst_4 s)) (Algebra.adjoin.{u1, u2} R A _inst_1 _inst_3 _inst_4 (Star.star.{u2} (Set.{u2} A) (Set.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5)))) s))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] (s : Set.{u2} A), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Star.star.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (InvolutiveStar.toStar.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Subalgebra.involutiveStar.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)) (Algebra.adjoin.{u1, u2} R A _inst_1 _inst_3 _inst_4 s)) (Algebra.adjoin.{u1, u2} R A _inst_1 _inst_3 _inst_4 (Star.star.{u2} (Set.{u2} A) (Set.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5)))) s))
+Case conversion may be inaccurate. Consider using '#align subalgebra.star_adjoin_comm Subalgebra.star_adjoin_commₓ'. -/
 /-- The star operation on `subalgebra` commutes with `algebra.adjoin`. -/
 theorem star_adjoin_comm (s : Set A) : star (Algebra.adjoin R s) = Algebra.adjoin R (star s) :=
   have this : ∀ t : Set A, Algebra.adjoin R (star t) ≤ star (Algebra.adjoin R t) := fun t =>
@@ -385,6 +649,7 @@ theorem star_adjoin_comm (s : Set A) : star (Algebra.adjoin R s) = Algebra.adjoi
 
 variable {R}
 
+#print Subalgebra.starClosure /-
 /-- The `star_subalgebra` obtained from `S : subalgebra R A` by taking the smallest subalgebra
 containing both `S` and `star S`. -/
 @[simps]
@@ -397,7 +662,14 @@ def starClosure (S : Subalgebra R A) : StarSubalgebra R A :=
       convert ha
       simp [Set.union_comm] }
 #align subalgebra.star_closure Subalgebra.starClosure
+-/
 
+/- warning: subalgebra.star_closure_le -> Subalgebra.starClosure_le 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S₁ : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂)) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂)
+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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S₁ : Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, (LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂)) -> (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂)
+Case conversion may be inaccurate. Consider using '#align subalgebra.star_closure_le Subalgebra.starClosure_leₓ'. -/
 theorem starClosure_le {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂.toSubalgebra) :
     S₁.starClosure ≤ S₂ :=
   StarSubalgebra.toSubalgebra_le_iff.1 <|
@@ -405,6 +677,12 @@ theorem starClosure_le {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} (h :
       (star_star x ▸ star_mem (show star x ∈ S₂ from h <| (S₁.mem_star_iff _).1 hx) : x ∈ S₂)
 #align subalgebra.star_closure_le Subalgebra.starClosure_le
 
+/- warning: subalgebra.star_closure_le_iff -> Subalgebra.starClosure_le_iff 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S₁ : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂) (LE.le.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteSemilatticeInf.toPartialOrder.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂))
+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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S₁ : Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4} {S₂ : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Subalgebra.starClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S₁) S₂) (LE.le.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Preorder.toLE.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (PartialOrder.toPreorder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4))))) S₁ (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S₂))
+Case conversion may be inaccurate. Consider using '#align subalgebra.star_closure_le_iff Subalgebra.starClosure_le_iffₓ'. -/
 theorem starClosure_le_iff {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} :
     S₁.starClosure ≤ S₂ ↔ S₁ ≤ S₂.toSubalgebra :=
   ⟨fun h => le_sup_left.trans h, starClosure_le⟩
@@ -425,6 +703,7 @@ variable [Semiring B] [Algebra R B] [StarRing B] [StarModule R B]
 
 variable (R)
 
+#print StarSubalgebra.adjoin /-
 /-- The minimal star subalgebra that contains `s`. -/
 @[simps]
 def adjoin (s : Set A) : StarSubalgebra R A :=
@@ -433,36 +712,55 @@ def adjoin (s : Set A) : StarSubalgebra R A :=
       rwa [Subalgebra.mem_carrier, ← Subalgebra.mem_star_iff, Subalgebra.star_adjoin_comm,
         Set.union_star, star_star, Set.union_comm] }
 #align star_subalgebra.adjoin StarSubalgebra.adjoin
+-/
 
+#print StarSubalgebra.adjoin_eq_starClosure_adjoin /-
 theorem adjoin_eq_starClosure_adjoin (s : Set A) : adjoin R s = (Algebra.adjoin R s).starClosure :=
   toSubalgebra_injective <|
     show Algebra.adjoin R (s ∪ star s) = Algebra.adjoin R s ⊔ star (Algebra.adjoin R s) from
       (Subalgebra.star_adjoin_comm R s).symm ▸ Algebra.adjoin_union s (star s)
 #align star_subalgebra.adjoin_eq_star_closure_adjoin StarSubalgebra.adjoin_eq_starClosure_adjoin
+-/
 
+#print StarSubalgebra.adjoin_toSubalgebra /-
 theorem adjoin_toSubalgebra (s : Set A) :
     (adjoin R s).toSubalgebra = Algebra.adjoin R (s ∪ star s) :=
   rfl
 #align star_subalgebra.adjoin_to_subalgebra StarSubalgebra.adjoin_toSubalgebra
+-/
 
+#print StarSubalgebra.subset_adjoin /-
 theorem subset_adjoin (s : Set A) : s ⊆ adjoin R s :=
   (Set.subset_union_left s (star s)).trans Algebra.subset_adjoin
 #align star_subalgebra.subset_adjoin StarSubalgebra.subset_adjoin
+-/
 
+#print StarSubalgebra.star_subset_adjoin /-
 theorem star_subset_adjoin (s : Set A) : star s ⊆ adjoin R s :=
   (Set.subset_union_right s (star s)).trans Algebra.subset_adjoin
 #align star_subalgebra.star_subset_adjoin StarSubalgebra.star_subset_adjoin
+-/
 
+#print StarSubalgebra.self_mem_adjoin_singleton /-
 theorem self_mem_adjoin_singleton (x : A) : x ∈ adjoin R ({x} : Set A) :=
   Algebra.subset_adjoin <| Set.mem_union_left _ (Set.mem_singleton x)
 #align star_subalgebra.self_mem_adjoin_singleton StarSubalgebra.self_mem_adjoin_singleton
+-/
 
+#print StarSubalgebra.star_self_mem_adjoin_singleton /-
 theorem star_self_mem_adjoin_singleton (x : A) : star x ∈ adjoin R ({x} : Set A) :=
   star_mem <| self_mem_adjoin_singleton R x
 #align star_subalgebra.star_self_mem_adjoin_singleton StarSubalgebra.star_self_mem_adjoin_singleton
+-/
 
 variable {R}
 
+/- warning: star_subalgebra.gc -> StarSubalgebra.gc 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))], GaloisConnection.{u2, u2} (Set.{u2} A) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (Set.{u2} A) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} A) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} A) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} A) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} A) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} A) (Set.completeBooleanAlgebra.{u2} A))))))) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) ((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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)], GaloisConnection.{u2, u2} (Set.{u2} A) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (Set.{u2} A) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} A) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} A) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} A) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} A) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} A) (Set.instCompleteBooleanAlgebraSet.{u2} A))))))) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.gc StarSubalgebra.gcₓ'. -/
 protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A) coe :=
   by
   intro s S
@@ -472,6 +770,12 @@ protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A
       Set.union_subset h fun x hx => star_star x ▸ star_mem (show star x ∈ S from h hx)⟩
 #align star_subalgebra.gc StarSubalgebra.gc
 
+/- warning: star_subalgebra.gi -> StarSubalgebra.gi 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))], GaloisInsertion.{u2, u2} (Set.{u2} A) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (Set.{u2} A) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} A) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} A) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} A) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} A) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} A) (Set.completeBooleanAlgebra.{u2} A))))))) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) ((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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)], GaloisInsertion.{u2, u2} (Set.{u2} A) (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (Set.{u2} A) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} A) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} A) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} A) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} A) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} A) (Set.instCompleteBooleanAlgebraSet.{u2} A))))))) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.gi StarSubalgebra.giₓ'. -/
 /-- Galois insertion between `adjoin` and `coe`. -/
 protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) coe
     where
@@ -481,20 +785,44 @@ protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) coe
   choice_eq _ _ := StarSubalgebra.copy_eq _ _ _
 #align star_subalgebra.gi StarSubalgebra.gi
 
+/- warning: star_subalgebra.adjoin_le -> StarSubalgebra.adjoin_le 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u2} A}, (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s ((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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) S)) -> (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u1} A}, (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) s (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S)) -> (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) S)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_le StarSubalgebra.adjoin_leₓ'. -/
 theorem adjoin_le {S : StarSubalgebra R A} {s : Set A} (hs : s ⊆ S) : adjoin R s ≤ S :=
   StarSubalgebra.gc.l_le hs
 #align star_subalgebra.adjoin_le StarSubalgebra.adjoin_le
 
+/- warning: star_subalgebra.adjoin_le_iff -> StarSubalgebra.adjoin_le_iff 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u2} A}, Iff (LE.le.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.partialOrder.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) S) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) s ((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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {s : Set.{u1} A}, Iff (LE.le.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instPartialOrder.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (StarSubalgebra.adjoin.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) S) (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) s (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_le_iff StarSubalgebra.adjoin_le_iffₓ'. -/
 theorem adjoin_le_iff {S : StarSubalgebra R A} {s : Set A} : adjoin R s ≤ S ↔ s ⊆ S :=
   StarSubalgebra.gc _ _
 #align star_subalgebra.adjoin_le_iff StarSubalgebra.adjoin_le_iff
 
+/- warning: subalgebra.star_closure_eq_adjoin -> Subalgebra.starClosure_eq_adjoin 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4), Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Subalgebra.starClosure.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.setLike.{u1, u2} R A _inst_1 _inst_3 _inst_4)))) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] (S : Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4), Eq.{succ u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Subalgebra.starClosure.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 S) (StarSubalgebra.adjoin.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (SetLike.coe.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) S))
+Case conversion may be inaccurate. Consider using '#align subalgebra.star_closure_eq_adjoin Subalgebra.starClosure_eq_adjoinₓ'. -/
 theorem Subalgebra.starClosure_eq_adjoin (S : Subalgebra R A) :
     S.starClosure = adjoin R (S : Set A) :=
   le_antisymm (Subalgebra.starClosure_le_iff.2 <| subset_adjoin R (S : Set A))
     (adjoin_le (le_sup_left : S ≤ S ⊔ star S))
 #align subalgebra.star_closure_eq_adjoin Subalgebra.starClosure_eq_adjoin
 
+/- warning: star_subalgebra.adjoin_induction -> StarSubalgebra.adjoin_induction 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {s : Set.{u2} A} {p : A -> Prop} {a : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) a (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (forall (x : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) x s) -> (p x)) -> (forall (r : R), p (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r)) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x y))) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x y))) -> (forall (x : A), (p x) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x))) -> (p a)
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {s : Set.{u2} A} {p : A -> Prop} {a : A}, (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) a (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) -> (forall (x : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) x s) -> (p x)) -> (forall (r : R), p (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4) r)) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x y))) -> (forall (x : A) (y : A), (p x) -> (p y) -> (p (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) x y))) -> (forall (x : A), (p x) -> (p (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x))) -> (p a)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_inductionₓ'. -/
 /-- If some predicate holds for all `x ∈ (s : set A)` and this predicate is closed under the
 `algebra_map`, addition, multiplication and star operations, then it holds for `a ∈ adjoin R s`. -/
 theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin R s)
@@ -506,6 +834,12 @@ theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin
     Hmul
 #align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_induction
 
+/- warning: star_subalgebra.adjoin_induction₂ -> StarSubalgebra.adjoin_induction₂ 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {s : Set.{u2} A} {p : A -> A -> Prop} {a : A} {b : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 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(StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) y))) -> (p a b)
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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 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(Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x) y)) -> (forall (x : A) (y : A), (p x y) -> (p x (Star.star.{u2} A (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) y))) -> (p a b)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂ₓ'. -/
 theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a ∈ adjoin R s)
     (hb : b ∈ adjoin R s) (Hs : ∀ x : A, x ∈ s → ∀ y : A, y ∈ s → p x y)
     (Halg : ∀ r₁ r₂ : R, p (algebraMap R A r₁) (algebraMap R A r₂))
@@ -531,6 +865,12 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
     exacts[Halg_right _ _ hx, star_star x ▸ Hstar_left _ _ (Halg_right r _ hx)]
 #align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂
 
+/- warning: star_subalgebra.adjoin_induction' -> StarSubalgebra.adjoin_induction' 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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 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+but is expected to have type
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_inst_5 _inst_6 s))), (p x) -> (p (Star.star.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) x))) -> (p a)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_induction' StarSubalgebra.adjoin_induction'ₓ'. -/
 /-- The difference with `star_subalgebra.adjoin_induction` is that this acts on the subtype. -/
 theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
     (Hs : ∀ (x) (h : x ∈ s), p ⟨x, subset_adjoin R s h⟩) (Halg : ∀ r, p (algebraMap R _ r))
@@ -550,6 +890,12 @@ theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
 
 variable (R)
 
+/- warning: star_subalgebra.adjoin_comm_semiring_of_comm -> StarSubalgebra.adjoinCommSemiringOfComm is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_comm_semiring_of_comm StarSubalgebra.adjoinCommSemiringOfCommₓ'. -/
 /-- If all elements of `s : set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `star_subalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
 @[reducible]
@@ -573,6 +919,12 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
       exact congr_arg coe (mul_comm (⟨x, hx⟩ : Algebra.adjoin R (s ∪ star s)) ⟨y, hy⟩) }
 #align star_subalgebra.adjoin_comm_semiring_of_comm StarSubalgebra.adjoinCommSemiringOfComm
 
+/- warning: star_subalgebra.adjoin_comm_ring_of_comm -> StarSubalgebra.adjoinCommRingOfComm is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13))] [_inst_16 : 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_11)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11))) _inst_12))) (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) (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_13))))))) (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_11)))))) (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_13))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11))) (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_13))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)))))] {s : Set.{u2} A}, (forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (forall (b : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13))) a b) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13))) b a)))) -> (forall (a : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) a s) -> (forall (b : A), (Membership.Mem.{u2, u2} A (Set.{u2} A) (Set.hasMem.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13))) a (Star.star.{u2} A (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) b)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13))) (Star.star.{u2} A (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) b) a)))) -> (CommRing.{u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 s)))
+but is expected to have type
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))] [_inst_16 : 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_11)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11))) _inst_12))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)] {s : Set.{u2} A}, (forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (forall (b : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))))) a b) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))))) b a)))) -> (forall (a : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) a s) -> (forall (b : A), (Membership.mem.{u2, u2} A (Set.{u2} A) (Set.instMembershipSet.{u2} A) b s) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))))) a (Star.star.{u2} A (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) b)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))))) (Star.star.{u2} A (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) b) a)))) -> (CommRing.{u2} (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) x (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 s))))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_comm_ring_of_comm StarSubalgebra.adjoinCommRingOfCommₓ'. -/
 /-- If all elements of `s : set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `star_subalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
 @[reducible]
@@ -585,6 +937,12 @@ def adjoinCommRingOfComm (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ri
     (adjoin R s).toSubalgebra.toRing with }
 #align star_subalgebra.adjoin_comm_ring_of_comm StarSubalgebra.adjoinCommRingOfComm
 
+/- warning: star_subalgebra.adjoin_comm_semiring_of_is_star_normal -> StarSubalgebra.adjoinCommSemiringOfIsStarNormal 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (x : A) [_inst_11 : IsStarNormal.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x], CommSemiring.{u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) x)))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] (x : A) [_inst_11 : IsStarNormal.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) x], CommSemiring.{u2} (Subtype.{succ u2} A (fun (x_1 : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x_1 (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) x))))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormalₓ'. -/
 /-- The star subalgebra `star_subalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
 instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
@@ -598,6 +956,12 @@ instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
     simpa only [ha, hb] using (star_comm_self' x).symm
 #align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormal
 
+/- warning: star_subalgebra.adjoin_comm_ring_of_is_star_normal -> StarSubalgebra.adjoinCommRingOfIsStarNormal is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13))] [_inst_16 : 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_11)))))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_11))) _inst_12))) (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) (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_13))))))) (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_11)))))) (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_13))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11))) (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_13))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)))))] (x : A) [_inst_17 : IsStarNormal.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A _inst_13)) (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_13))))) (StarRing.toStarAddMonoid.{u2} A (NonUnitalRing.toNonUnitalSemiring.{u2} A (Ring.toNonUnitalRing.{u2} A _inst_13)) _inst_15))) x], CommRing.{u2} (coeSort.{succ u2, succ (succ u2)} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) x)))
+but is expected to have type
+  forall (R : Type.{u1}) {A : Type.{u2}} [_inst_11 : CommRing.{u1} R] [_inst_12 : StarRing.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11)))] [_inst_13 : Ring.{u2} A] [_inst_14 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13)] [_inst_15 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13))] [_inst_16 : 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_11)))) (StarRing.toStarAddMonoid.{u1} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} R (CommSemiring.toNonUnitalCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_11))) _inst_12))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) (Ring.toSemiring.{u2} A _inst_13) _inst_14)] (x : A) [_inst_17 : IsStarNormal.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)))) (InvolutiveStar.toStar.{u2} A (StarAddMonoid.toInvolutiveStar.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddGroupWithOne.toAddMonoidWithOne.{u2} A (Ring.toAddGroupWithOne.{u2} A _inst_13))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A (Ring.toSemiring.{u2} A _inst_13)) _inst_15))) x], CommRing.{u2} (Subtype.{succ u2} A (fun (x_1 : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16) A (StarSubalgebra.setLike.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_15 _inst_14 _inst_16)) x_1 (StarSubalgebra.adjoin.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_11) _inst_12 (Ring.toSemiring.{u2} A _inst_13) _inst_14 _inst_15 _inst_16 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) x))))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.adjoin_comm_ring_of_is_star_normal StarSubalgebra.adjoinCommRingOfIsStarNormalₓ'. -/
 /-- The star subalgebra `star_subalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
 instance adjoinCommRingOfIsStarNormal (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ring A]
@@ -617,104 +981,230 @@ instance : CompleteLattice (StarSubalgebra R A) :=
 instance : Inhabited (StarSubalgebra R A) :=
   ⟨⊤⟩
 
+/- warning: star_subalgebra.coe_top -> StarSubalgebra.coe_top 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))], 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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Top.top.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Set.univ.{u2} A)
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)], Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Top.top.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Set.univ.{u2} A)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_top StarSubalgebra.coe_topₓ'. -/
 @[simp]
 theorem coe_top : (↑(⊤ : StarSubalgebra R A) : Set A) = Set.univ :=
   rfl
 #align star_subalgebra.coe_top StarSubalgebra.coe_top
 
+/- warning: star_subalgebra.mem_top -> StarSubalgebra.mem_top 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {x : A}, Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Top.top.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {x : A}, Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Top.top.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_top StarSubalgebra.mem_topₓ'. -/
 @[simp]
 theorem mem_top {x : A} : x ∈ (⊤ : StarSubalgebra R A) :=
   Set.mem_univ x
 #align star_subalgebra.mem_top StarSubalgebra.mem_top
 
+/- warning: star_subalgebra.top_to_subalgebra -> StarSubalgebra.top_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))], Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (Top.top.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)], Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (Top.top.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.top_to_subalgebra StarSubalgebra.top_toSubalgebraₓ'. -/
 @[simp]
 theorem top_toSubalgebra : (⊤ : StarSubalgebra R A).toSubalgebra = ⊤ :=
   rfl
 #align star_subalgebra.top_to_subalgebra StarSubalgebra.top_toSubalgebra
 
+/- warning: star_subalgebra.to_subalgebra_eq_top -> StarSubalgebra.toSubalgebra_eq_top 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S) (Top.top.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toHasTop.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4)))) (Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S (Top.top.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))
+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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S) (Top.top.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toTop.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4)))) (Eq.{succ u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S (Top.top.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.to_subalgebra_eq_top StarSubalgebra.toSubalgebra_eq_topₓ'. -/
 @[simp]
 theorem toSubalgebra_eq_top {S : StarSubalgebra R A} : S.toSubalgebra = ⊤ ↔ S = ⊤ :=
   StarSubalgebra.toSubalgebra_injective.eq_iff' top_toSubalgebra
 #align star_subalgebra.to_subalgebra_eq_top StarSubalgebra.toSubalgebra_eq_top
 
+/- warning: star_subalgebra.mem_sup_left -> StarSubalgebra.mem_sup_left 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {T : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {x : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x S) -> (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Sup.sup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeSup.toHasSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {T : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {x : A}, (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x S) -> (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Sup.sup.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeSup.toSup.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeSup.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) S T))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_sup_left StarSubalgebra.mem_sup_leftₓ'. -/
 theorem mem_sup_left {S T : StarSubalgebra R A} : ∀ {x : A}, x ∈ S → x ∈ S ⊔ T :=
   show S ≤ S ⊔ T from le_sup_left
 #align star_subalgebra.mem_sup_left StarSubalgebra.mem_sup_left
 
+/- warning: star_subalgebra.mem_sup_right -> StarSubalgebra.mem_sup_right 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {T : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {x : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x T) -> (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Sup.sup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeSup.toHasSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {T : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {x : A}, (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x T) -> (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Sup.sup.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeSup.toSup.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeSup.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) S T))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_sup_right StarSubalgebra.mem_sup_rightₓ'. -/
 theorem mem_sup_right {S T : StarSubalgebra R A} : ∀ {x : A}, x ∈ T → x ∈ S ⊔ T :=
   show T ≤ S ⊔ T from le_sup_right
 #align star_subalgebra.mem_sup_right StarSubalgebra.mem_sup_right
 
+/- warning: star_subalgebra.mul_mem_sup -> StarSubalgebra.mul_mem_sup 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {T : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {x : A} {y : A}, (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x S) -> (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) y T) -> (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) x y) (Sup.sup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeSup.toHasSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {T : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {x : A} {y : A}, (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x S) -> (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) y T) -> (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_3)))) x y) (Sup.sup.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeSup.toSup.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeSup.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) S T))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mul_mem_sup StarSubalgebra.mul_mem_supₓ'. -/
 theorem mul_mem_sup {S T : StarSubalgebra R A} {x y : A} (hx : x ∈ S) (hy : y ∈ T) :
     x * y ∈ S ⊔ T :=
   mul_mem (mem_sup_left hx) (mem_sup_right hy)
 #align star_subalgebra.mul_mem_sup StarSubalgebra.mul_mem_sup
 
+/- warning: star_subalgebra.map_sup -> StarSubalgebra.map_sup 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_10 : StarModule.{u1, u3} R B (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.{u3} B (StarAddMonoid.toHasInvolutiveStar.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_8)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (T : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (Sup.sup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeSup.toHasSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeSup.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) S T)) (Sup.sup.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (SemilatticeSup.toHasSup.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (Lattice.toSemilatticeSup.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (ConditionallyCompleteLattice.toLattice.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (CompleteLattice.toConditionallyCompleteLattice.{u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.completeLattice.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10))))) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f S) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f T))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u2} A] [_inst_4 : Algebra.{u3, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : StarModule.{u3, u2} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u2} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u3, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] [_inst_10 : StarModule.{u3, u1} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u2, u1} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))) (S : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (T : StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), Eq.{succ u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (Sup.sup.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeSup.toSup.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeSup.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) S T)) (Sup.sup.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (SemilatticeSup.toSup.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (Lattice.toSemilatticeSup.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (ConditionallyCompleteLattice.toLattice.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.completeLattice.{u3, u1} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10))))) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f S) (StarSubalgebra.map.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f T))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.map_sup StarSubalgebra.map_supₓ'. -/
 theorem map_sup (f : A →⋆ₐ[R] B) (S T : StarSubalgebra R A) : map f (S ⊔ T) = map f S ⊔ map f T :=
   (StarSubalgebra.gc_map_comap f).l_sup
 #align star_subalgebra.map_sup StarSubalgebra.map_sup
 
+/- warning: star_subalgebra.coe_inf -> StarSubalgebra.coe_inf is a dubious translation:
+lean 3 declaration is
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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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] (S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (T : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Inf.inf.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toInf.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S T)) (Inter.inter.{u1} (Set.{u1} A) (Set.instInterSet.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S) (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) T))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_inf StarSubalgebra.coe_infₓ'. -/
 @[simp, norm_cast]
 theorem coe_inf (S T : StarSubalgebra R A) : (↑(S ⊓ T) : Set A) = S ∩ T :=
   rfl
 #align star_subalgebra.coe_inf StarSubalgebra.coe_inf
 
+/- warning: star_subalgebra.mem_inf -> StarSubalgebra.mem_inf 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {T : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {x : A}, Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Inf.inf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeInf.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) S T)) (And (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x S) (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {T : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6} {x : A}, Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (Inf.inf.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toInf.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S T)) (And (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x S) (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x T))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_inf StarSubalgebra.mem_infₓ'. -/
 @[simp]
 theorem mem_inf {S T : StarSubalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S ∧ x ∈ T :=
   Iff.rfl
 #align star_subalgebra.mem_inf StarSubalgebra.mem_inf
 
+/- warning: star_subalgebra.inf_to_subalgebra -> StarSubalgebra.inf_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (T : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (Inf.inf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SemilatticeInf.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toSemilatticeInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) S T)) (Inf.inf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (SemilatticeInf.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Lattice.toSemilatticeInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))))) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] (S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (T : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (Inf.inf.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Lattice.toInf.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) S T)) (Inf.inf.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Lattice.toInf.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4)))) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 S) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 T))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.inf_to_subalgebra StarSubalgebra.inf_toSubalgebraₓ'. -/
 @[simp]
 theorem inf_toSubalgebra (S T : StarSubalgebra R A) :
     (S ⊓ T).toSubalgebra = S.toSubalgebra ⊓ T.toSubalgebra :=
   rfl
 #align star_subalgebra.inf_to_subalgebra StarSubalgebra.inf_toSubalgebra
 
+/- warning: star_subalgebra.coe_Inf -> StarSubalgebra.coe_infₛ 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), 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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (Set.interᵢ.{u2, succ u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (fun (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) => Set.interᵢ.{u2, 0} A (Membership.Mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.hasMem.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) (fun (H : Membership.Mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.hasMem.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) => (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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) s)))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (Set.interᵢ.{u2, succ u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (fun (s : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) => Set.interᵢ.{u2, 0} A (Membership.mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.instMembershipSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) (fun (H : Membership.mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.instMembershipSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) s S) => SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) s)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_Inf StarSubalgebra.coe_infₛₓ'. -/
 @[simp, norm_cast]
 theorem coe_infₛ (S : Set (StarSubalgebra R A)) : (↑(infₛ S) : Set A) = ⋂ s ∈ S, ↑s :=
   infₛ_image
 #align star_subalgebra.coe_Inf StarSubalgebra.coe_infₛ
 
+/- warning: star_subalgebra.mem_Inf -> StarSubalgebra.mem_infₛ 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (forall (p : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), (Membership.Mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.hasMem.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) p S) -> (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x p))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] {S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (forall (p : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6), (Membership.mem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) (Set.instMembershipSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) p S) -> (Membership.mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x p))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_Inf StarSubalgebra.mem_infₛₓ'. -/
 theorem mem_infₛ {S : Set (StarSubalgebra R A)} {x : A} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p := by
   simp only [← SetLike.mem_coe, coe_Inf, Set.mem_interᵢ₂]
 #align star_subalgebra.mem_Inf StarSubalgebra.mem_infₛ
 
+/- warning: star_subalgebra.Inf_to_subalgebra -> StarSubalgebra.infₛ_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))) (Set.image.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)] (S : Set.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (InfSet.infₛ.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) S)) (InfSet.infₛ.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toInfSet.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4))) (Set.image.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.Inf_to_subalgebra StarSubalgebra.infₛ_toSubalgebraₓ'. -/
 @[simp]
 theorem infₛ_toSubalgebra (S : Set (StarSubalgebra R A)) :
     (infₛ S).toSubalgebra = infₛ (StarSubalgebra.toSubalgebra '' S) :=
   SetLike.coe_injective <| by simp
 #align star_subalgebra.Inf_to_subalgebra StarSubalgebra.infₛ_toSubalgebra
 
+/- warning: star_subalgebra.coe_infi -> StarSubalgebra.coe_infᵢ 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)}, 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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (infᵢ.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (Set.interᵢ.{u2, u3} A ι (fun (i : ι) => (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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (S i)))
+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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)}, Eq.{succ u1} (Set.{u1} A) (SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (infᵢ.{u1, u3} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (Set.interᵢ.{u1, u3} A ι (fun (i : ι) => SetLike.coe.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (S i)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_infi StarSubalgebra.coe_infᵢₓ'. -/
 @[simp, norm_cast]
 theorem coe_infᵢ {ι : Sort _} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
   simp [infᵢ]
 #align star_subalgebra.coe_infi StarSubalgebra.coe_infᵢ
 
+/- warning: star_subalgebra.mem_infi -> StarSubalgebra.mem_infᵢ 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (infᵢ.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (S i))
+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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {ι : Sort.{u3}} {S : ι -> (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)} {x : A}, Iff (Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (infᵢ.{u1, u3} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (forall (i : ι), Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (S i))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_infi StarSubalgebra.mem_infᵢₓ'. -/
 theorem mem_infᵢ {ι : Sort _} {S : ι → StarSubalgebra R A} {x : A} :
     (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [infᵢ, mem_Inf, Set.forall_range_iff]
 #align star_subalgebra.mem_infi StarSubalgebra.mem_infᵢ
 
+/- warning: star_subalgebra.infi_to_subalgebra -> StarSubalgebra.infᵢ_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {ι : Sort.{u3}} (S : ι -> (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (infᵢ.{u2, u3} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toHasInf.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (infᵢ.{u2, u3} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toHasInf.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (S i)))
+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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {ι : Sort.{u3}} (S : ι -> (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)), Eq.{succ u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (infᵢ.{u1, u3} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (ConditionallyCompleteLattice.toInfSet.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toConditionallyCompleteLattice.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))) ι (fun (i : ι) => S i))) (infᵢ.{u1, u3} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (ConditionallyCompleteLattice.toInfSet.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u2, u1} R A _inst_1 _inst_3 _inst_4))) ι (fun (i : ι) => StarSubalgebra.toSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (S i)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.infi_to_subalgebra StarSubalgebra.infᵢ_toSubalgebraₓ'. -/
 @[simp]
 theorem infᵢ_toSubalgebra {ι : Sort _} (S : ι → StarSubalgebra R A) :
     (⨅ i, S i).toSubalgebra = ⨅ i, (S i).toSubalgebra :=
   SetLike.coe_injective <| by simp
 #align star_subalgebra.infi_to_subalgebra StarSubalgebra.infᵢ_toSubalgebra
 
+/- warning: star_subalgebra.bot_to_subalgebra -> StarSubalgebra.bot_toSubalgebra 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))], Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toHasBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.Subalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)], Eq.{succ u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (StarSubalgebra.toSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Bot.bot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (CompleteLattice.toBot.{u2} (Subalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4) (Algebra.instCompleteLatticeSubalgebra.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.bot_to_subalgebra StarSubalgebra.bot_toSubalgebraₓ'. -/
 theorem bot_toSubalgebra : (⊥ : StarSubalgebra R A).toSubalgebra = ⊥ :=
   by
   change Algebra.adjoin R (∅ ∪ star ∅) = Algebra.adjoin R ∅
   simp
 #align star_subalgebra.bot_to_subalgebra StarSubalgebra.bot_toSubalgebra
 
+/- warning: star_subalgebra.mem_bot -> StarSubalgebra.mem_bot is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align star_subalgebra.mem_bot StarSubalgebra.mem_botₓ'. -/
 theorem mem_bot {x : A} : x ∈ (⊥ : StarSubalgebra R A) ↔ x ∈ Set.range (algebraMap R A) := by
   rw [← mem_to_subalgebra, bot_to_subalgebra, Algebra.mem_bot]
 #align star_subalgebra.mem_bot StarSubalgebra.mem_bot
 
+/- warning: star_subalgebra.coe_bot -> StarSubalgebra.coe_bot 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))], 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_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)))) (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Set.range.{u2, succ u1} A R (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
+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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_3 _inst_4)], Eq.{succ u2} (Set.{u2} A) (SetLike.coe.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Bot.bot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toBot.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (Set.range.{u2, succ u1} A R (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_3))))) (algebraMap.{u1, u2} R A _inst_1 _inst_3 _inst_4)))
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.coe_bot StarSubalgebra.coe_botₓ'. -/
 @[simp]
 theorem coe_bot : ((⊥ : StarSubalgebra R A) : Set A) = Set.range (algebraMap R A) := by
   simp [Set.ext_iff, mem_bot]
 #align star_subalgebra.coe_bot StarSubalgebra.coe_bot
 
+/- warning: star_subalgebra.eq_top_iff -> StarSubalgebra.eq_top_iff 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] {S : StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (Eq.{succ u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S (Top.top.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (forall (x : A), Membership.Mem.{u2, u2} A (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.hasMem.{u2, u2} (StarSubalgebra.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) 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 : Semiring.{u1} A] [_inst_4 : Algebra.{u2, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u1} R A _inst_1 _inst_3 _inst_4)] {S : StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6}, Iff (Eq.{succ u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) S (Top.top.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) (forall (x : A), Membership.mem.{u1, u1} A (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u1, u1} (StarSubalgebra.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u1} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x S)
+Case conversion may be inaccurate. Consider using '#align star_subalgebra.eq_top_iff StarSubalgebra.eq_top_iffₓ'. -/
 theorem eq_top_iff {S : StarSubalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=
   ⟨fun h x => by rw [h] <;> exact mem_top, fun h => by
     ext x <;> exact ⟨fun _ => mem_top, fun _ => h x⟩⟩
@@ -736,6 +1226,7 @@ variable [hF : StarAlgHomClass F R A B] (f g : F)
 
 include hF
 
+#print StarAlgHom.equalizer /-
 /-- The equalizer of two star `R`-algebra homomorphisms. -/
 def equalizer : StarSubalgebra R A
     where
@@ -747,28 +1238,59 @@ def equalizer : StarSubalgebra R A
   algebraMap_mem' r := by simp only [Set.mem_setOf_eq, AlgHomClass.commutes]
   star_mem' a (ha : f a = g a) := by rw [Set.mem_setOf_eq, map_star f, map_star g, ha]
 #align star_alg_hom.equalizer StarAlgHom.equalizer
+-/
 
+/- warning: star_alg_hom.mem_equalizer -> StarAlgHom.mem_equalizer is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A 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_inst_4 _inst_6)) x (StarAlgHom.equalizer.{u1, u2, u3, u4} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g)) (Eq.{succ u4} B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B 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+but is expected to have type
+  forall {F : Type.{u2}} {R : Type.{u3}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u3, u4} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A 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(StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) hF)) g x))
+Case conversion may be inaccurate. Consider using '#align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizerₓ'. -/
 @[simp]
 theorem mem_equalizer (x : A) : x ∈ StarAlgHom.equalizer f g ↔ f x = g x :=
   Iff.rfl
 #align star_alg_hom.mem_equalizer StarAlgHom.mem_equalizer
 
+/- warning: star_alg_hom.adjoin_le_equalizer -> StarAlgHom.adjoin_le_equalizer is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u3} A}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A 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A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) f) (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B 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_inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+but is expected to have type
+  forall {F : Type.{u2}} {R : Type.{u1}} {A : Type.{u4}} {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 : Semiring.{u4} A] [_inst_4 : Algebra.{u1, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u1, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u1, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [hF : StarAlgHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))] (f : F) (g : F) {s : Set.{u4} A}, (Set.EqOn.{u4, u3} A B (FunLike.coe.{succ u2, succ u4, succ u3} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u3} B (StarAddMonoid.toInvolutiveStar.{u3} B (AddMonoidWithOne.toAddMonoid.{u3} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} B (NonAssocSemiring.toAddCommMonoidWithOne.{u3} 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(x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{u2, u4, u3} F A B (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u2, u1, u4, u3} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9))) hF)) g) s) -> (LE.le.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (Preorder.toLE.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (PartialOrder.toPreorder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (OmegaCompletePartialOrder.toPartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.instOmegaCompletePartialOrder.{u4} (StarSubalgebra.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6))))) (StarSubalgebra.adjoin.{u1, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (StarAlgHom.equalizer.{u2, u1, u4, u3} F R A B _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 _inst_8 _inst_9 hF f g))
+Case conversion may be inaccurate. Consider using '#align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizerₓ'. -/
 theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAlgHom.equalizer f g :=
   adjoin_le h
 #align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizer
 
+/- warning: star_alg_hom.ext_of_adjoin_eq_top -> StarAlgHom.ext_of_adjoin_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] [hF : StarAlgHomClass.{u1, u2, u3, u4} F R A B _inst_1 _inst_3 _inst_4 (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9)))] {s : Set.{u3} A}, (Eq.{succ u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toHasTop.{u3} (StarSubalgebra.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u2, u3} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u3, u4} A B (coeFn.{succ u1, max (succ u3) (succ u4)} F (fun (_x : F) => A -> B) (FunLike.hasCoeToFun.{succ u1, succ u3, succ u4} F A (fun (_x : A) => B) (StarHomClass.toFunLike.{u1, u3, u4} F A B (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B 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(InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toHasStar.{u4} B (StarAddMonoid.toHasInvolutiveStar.{u4} B (AddCommMonoid.toAddMonoid.{u4} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u4} B (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)))) (StarRing.toStarAddMonoid.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7) _inst_9))) hF))) g) s) -> (Eq.{succ u1} F f g))
+but is expected to have type
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(AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))] {s : Set.{u4} A}, (Eq.{succ u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s) (Top.top.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (CompleteLattice.toTop.{u4} (StarSubalgebra.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.completeLattice.{u3, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6)))) -> (forall {{f : F}} {{g : F}}, (Set.EqOn.{u4, u2} A B (FunLike.coe.{succ u1, succ u4, succ u2} F A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{u1, u4, u2} F A B (InvolutiveStar.toStar.{u4} A 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(StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) hF)) g) s) -> (Eq.{succ u1} F f g))
+Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_topₓ'. -/
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
   FunLike.ext f g fun x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
 #align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_top
 
 omit hF
 
+/- warning: star_alg_hom.map_adjoin -> StarAlgHom.map_adjoin 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 : Semiring.{u2} A] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3)] [_inst_6 : 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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _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_3)))))) (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_3)))))) (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_3)))))) (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_3))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u3} B] [_inst_8 : Algebra.{u1, u3} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7)] [_inst_10 : StarModule.{u1, u3} R B (InvolutiveStar.toHasStar.{u1} R (StarAddMonoid.toHasInvolutiveStar.{u1} R (AddCommMonoid.toAddMonoid.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_7))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_7 _inst_8)))))] (f : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (s : Set.{u2} A), Eq.{succ u3} (StarSubalgebra.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u1, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u1, u3} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u2, u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) (fun (_x : StarAlgHom.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) => A -> B) (StarAlgHom.hasCoeToFun.{u1, u2, u3} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) _inst_7 _inst_8 (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_7)))) (StarRing.toStarAddMonoid.{u3} B (Semiring.toNonUnitalSemiring.{u3} B _inst_7) _inst_9)))) f) s))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : StarRing.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1))] [_inst_3 : Semiring.{u1} A] [_inst_4 : Algebra.{u3, u1} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3)] [_inst_6 : StarModule.{u3, u1} R A (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} 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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (Algebra.toSMul.{u3, u1} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u2} B] [_inst_8 : Algebra.{u3, u2} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7)] [_inst_10 : StarModule.{u3, u2} R B (InvolutiveStar.toStar.{u3} R (StarAddMonoid.toInvolutiveStar.{u3} R (AddMonoidWithOne.toAddMonoid.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (StarRing.toStarAddMonoid.{u3} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} R (CommSemiring.toNonUnitalCommSemiring.{u3} R _inst_1)) _inst_2))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_7 _inst_8)] (f : StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) (s : Set.{u1} A), Eq.{succ u2} (StarSubalgebra.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_9 _inst_8 _inst_10) (StarSubalgebra.map.{u3, u1, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 _inst_7 _inst_9 _inst_8 _inst_10 f (StarSubalgebra.adjoin.{u3, u1} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarSubalgebra.adjoin.{u3, u2} R B _inst_1 _inst_2 _inst_7 _inst_8 _inst_9 _inst_10 (Set.image.{u1, u2} A B (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : A) => B) _x) (StarHomClass.toFunLike.{max u1 u2, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) A B (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{max u1 u2, u3, u1, u2} (StarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))) R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9))) (StarAlgHom.instStarAlgHomClassStarAlgHom.{u3, u1, u2} R A B _inst_1 _inst_3 _inst_4 (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_3)))) (StarRing.toStarAddMonoid.{u1} A (Semiring.toNonUnitalSemiring.{u1} A _inst_3) _inst_5))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u2} B (StarAddMonoid.toInvolutiveStar.{u2} B (AddMonoidWithOne.toAddMonoid.{u2} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} B (NonAssocSemiring.toAddCommMonoidWithOne.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_7)))) (StarRing.toStarAddMonoid.{u2} B (Semiring.toNonUnitalSemiring.{u2} B _inst_7) _inst_9)))))) f) s))
+Case conversion may be inaccurate. Consider using '#align star_alg_hom.map_adjoin StarAlgHom.map_adjoinₓ'. -/
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
   GaloisConnection.l_comm_of_u_comm Set.image_preimage (gc_map_comap f) StarSubalgebra.gc
     StarSubalgebra.gc fun _ => rfl
 #align star_alg_hom.map_adjoin StarAlgHom.map_adjoin
 
+/- warning: star_alg_hom.ext_adjoin -> StarAlgHom.ext_adjoin is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {s : Set.{u3} A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A 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+but is expected to have type
+  forall {F : Type.{u3}} {R : Type.{u2}} {A : Type.{u4}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : StarRing.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))] [_inst_3 : Semiring.{u4} A] [_inst_4 : Algebra.{u2, u4} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3)] [_inst_6 : StarModule.{u2, u4} 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.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (Algebra.toSMul.{u2, u4} R A _inst_1 _inst_3 _inst_4)] [_inst_7 : Semiring.{u1} B] [_inst_8 : Algebra.{u2, u1} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7)] {s : Set.{u4} A} [_inst_10 : StarAlgHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9)))] {f : F} {g : F}, (forall (x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))), (Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) (Subtype.val.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (Set.{u4} A) (Set.instMembershipSet.{u4} A) x (SetLike.coe.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) x) s) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => 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_inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) f x) (FunLike.coe.{succ u3, succ u4, succ u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (fun (_x : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) => B) _x) (StarHomClass.toFunLike.{u3, u4, u1} F (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u3, u2, u4, u1} F R (Subtype.{succ u4} A (fun (x : A) => Membership.mem.{u4, u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u4, u4} (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) B _inst_1 (Subalgebra.toSemiring.{u2, u4} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s))) (StarSubalgebra.algebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) (StarMemClass.instStarSubtypeMemInstMembership.{u4} A (StarSubalgebra.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (InvolutiveStar.toStar.{u4} A (StarAddMonoid.toInvolutiveStar.{u4} A (AddMonoidWithOne.toAddMonoid.{u4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_3)))) (StarRing.toStarAddMonoid.{u4} A (Semiring.toNonUnitalSemiring.{u4} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u2, u4} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 s)) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g x))) -> (Eq.{succ u3} F f g)
+Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoinₓ'. -/
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g :=
   by
@@ -783,6 +1305,12 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
   · rw [map_star, map_star, hx]
 #align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoin
 
+/- warning: star_alg_hom.ext_adjoin_singleton -> StarAlgHom.ext_adjoin_singleton is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {R : Type.{u2}} {A : Type.{u3}} {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 : Semiring.{u3} A] [_inst_4 : Algebra.{u2, u3} R A _inst_1 _inst_3] [_inst_5 : StarRing.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)] [_inst_6 : StarModule.{u2, u3} R A (InvolutiveStar.toHasStar.{u2} R (StarAddMonoid.toHasInvolutiveStar.{u2} R (AddCommMonoid.toAddMonoid.{u2} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1))))) (StarRing.toStarAddMonoid.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (CommSemiring.toNonUnitalCommSemiring.{u2} R _inst_1)) _inst_2))) (InvolutiveStar.toHasStar.{u3} A (StarAddMonoid.toHasInvolutiveStar.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3)))) (StarRing.toStarAddMonoid.{u3} A (Semiring.toNonUnitalSemiring.{u3} A _inst_3) _inst_5))) (SMulZeroClass.toHasSmul.{u2, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} R A (MulZeroClass.toHasZero.{u2} R (MulZeroOneClass.toMulZeroClass.{u2} R (MonoidWithZero.toMulZeroOneClass.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} R A (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_3 _inst_4)))))] [_inst_7 : Semiring.{u4} B] [_inst_8 : Algebra.{u2, u4} R B _inst_1 _inst_7] [_inst_9 : StarRing.{u4} B (Semiring.toNonUnitalSemiring.{u4} B _inst_7)] {a : A} [_inst_10 : StarAlgHomClass.{u1, u2, u3, u4} F R (coeSort.{succ u3, succ (succ u3)} (StarSubalgebra.{u2, u3} R A _inst_1 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_inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u1} F f g)
+but is expected to have type
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a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A 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_inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => (fun (x._@.Mathlib.Algebra.Star.Basic._hyg.3016 : Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) => B) _x) (StarHomClass.toFunLike.{u4, u2, u1} F (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) (StarAlgHomClass.toStarHomClass.{u4, u3, u2, u1} F R (Subtype.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) B _inst_1 (Subalgebra.toSemiring.{u3, u2} R A _inst_1 _inst_3 _inst_4 (StarSubalgebra.toSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a)))) (StarSubalgebra.algebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6 (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) (StarMemClass.instStarSubtypeMemInstMembership.{u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (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_3)))) (StarRing.toStarAddMonoid.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_3) _inst_5))) (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.starMemClass.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) _inst_7 _inst_8 (InvolutiveStar.toStar.{u1} B (StarAddMonoid.toInvolutiveStar.{u1} B (AddMonoidWithOne.toAddMonoid.{u1} B (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} B (NonAssocSemiring.toAddCommMonoidWithOne.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_7)))) (StarRing.toStarAddMonoid.{u1} B (Semiring.toNonUnitalSemiring.{u1} B _inst_7) _inst_9))) _inst_10)) g (Subtype.mk.{succ u2} A (fun (x : A) => Membership.mem.{u2, u2} A (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) (SetLike.instMembership.{u2, u2} (StarSubalgebra.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6) A (StarSubalgebra.setLike.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_5 _inst_4 _inst_6)) x (StarSubalgebra.adjoin.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) a))) a (StarSubalgebra.self_mem_adjoin_singleton.{u3, u2} R A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 a)))) -> (Eq.{succ u4} F f g)
+Case conversion may be inaccurate. Consider using '#align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singletonₓ'. -/
 theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
     (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=
   ext_adjoin fun x hx =>

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

All these are about some code (now commented out) which performs a (now) redundant binder information update. I don't see how this is useful information going forward, hence propose simply deleting them.

@@ -291,7 +291,7 @@ end Map
 
 section Centralizer
 
-variable (R) -- Porting note: redundant binder annotation update
+variable (R)
 
 /-- The centralizer, or commutant, of the star-closure of a set as a star subalgebra. -/
 def centralizer (s : Set A) : StarSubalgebra R A where

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

@@ -410,7 +410,9 @@ end Subalgebra
 /-! ### The star subalgebra generated by a set -/
 
 
-namespace StarSubalgebra
+namespace StarAlgebra
+
+open StarSubalgebra
 
 variable {F R A B : Type*} [CommSemiring R] [StarRing R]
 variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
@@ -424,35 +426,35 @@ def adjoin (s : Set A) : StarSubalgebra R A :=
     star_mem' := fun hx => by
       rwa [Subalgebra.mem_carrier, ← Subalgebra.mem_star_iff, Subalgebra.star_adjoin_comm,
         Set.union_star, star_star, Set.union_comm] }
-#align star_subalgebra.adjoin StarSubalgebra.adjoin
+#align star_subalgebra.adjoin StarAlgebra.adjoin
 
 theorem adjoin_eq_starClosure_adjoin (s : Set A) : adjoin R s = (Algebra.adjoin R s).starClosure :=
   toSubalgebra_injective <|
     show Algebra.adjoin R (s ∪ star s) = Algebra.adjoin R s ⊔ star (Algebra.adjoin R s) from
       (Subalgebra.star_adjoin_comm R s).symm ▸ Algebra.adjoin_union s (star s)
-#align star_subalgebra.adjoin_eq_star_closure_adjoin StarSubalgebra.adjoin_eq_starClosure_adjoin
+#align star_subalgebra.adjoin_eq_star_closure_adjoin StarAlgebra.adjoin_eq_starClosure_adjoin
 
 theorem adjoin_toSubalgebra (s : Set A) :
     (adjoin R s).toSubalgebra = Algebra.adjoin R (s ∪ star s) :=
   rfl
-#align star_subalgebra.adjoin_to_subalgebra StarSubalgebra.adjoin_toSubalgebra
+#align star_subalgebra.adjoin_to_subalgebra StarAlgebra.adjoin_toSubalgebra
 
 @[aesop safe 20 apply (rule_sets := [SetLike])]
 theorem subset_adjoin (s : Set A) : s ⊆ adjoin R s :=
   (Set.subset_union_left s (star s)).trans Algebra.subset_adjoin
-#align star_subalgebra.subset_adjoin StarSubalgebra.subset_adjoin
+#align star_subalgebra.subset_adjoin StarAlgebra.subset_adjoin
 
 theorem star_subset_adjoin (s : Set A) : star s ⊆ adjoin R s :=
   (Set.subset_union_right s (star s)).trans Algebra.subset_adjoin
-#align star_subalgebra.star_subset_adjoin StarSubalgebra.star_subset_adjoin
+#align star_subalgebra.star_subset_adjoin StarAlgebra.star_subset_adjoin
 
 theorem self_mem_adjoin_singleton (x : A) : x ∈ adjoin R ({x} : Set A) :=
   Algebra.subset_adjoin <| Set.mem_union_left _ (Set.mem_singleton x)
-#align star_subalgebra.self_mem_adjoin_singleton StarSubalgebra.self_mem_adjoin_singleton
+#align star_subalgebra.self_mem_adjoin_singleton StarAlgebra.self_mem_adjoin_singleton
 
 theorem star_self_mem_adjoin_singleton (x : A) : star x ∈ adjoin R ({x} : Set A) :=
   star_mem <| self_mem_adjoin_singleton R x
-#align star_subalgebra.star_self_mem_adjoin_singleton StarSubalgebra.star_self_mem_adjoin_singleton
+#align star_subalgebra.star_self_mem_adjoin_singleton StarAlgebra.star_self_mem_adjoin_singleton
 
 variable {R}
 
@@ -462,23 +464,23 @@ protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A
   exact
     ⟨fun h => (Set.subset_union_left s _).trans h, fun h =>
       Set.union_subset h fun x hx => star_star x ▸ star_mem (show star x ∈ S from h hx)⟩
-#align star_subalgebra.gc StarSubalgebra.gc
+#align star_subalgebra.gc StarAlgebra.gc
 
 /-- Galois insertion between `adjoin` and `coe`. -/
 protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) (↑) where
-  choice s hs := (adjoin R s).copy s <| le_antisymm (StarSubalgebra.gc.le_u_l s) hs
-  gc := StarSubalgebra.gc
-  le_l_u S := (StarSubalgebra.gc (S : Set A) (adjoin R S)).1 <| le_rfl
+  choice s hs := (adjoin R s).copy s <| le_antisymm (StarAlgebra.gc.le_u_l s) hs
+  gc := StarAlgebra.gc
+  le_l_u S := (StarAlgebra.gc (S : Set A) (adjoin R S)).1 <| le_rfl
   choice_eq _ _ := StarSubalgebra.copy_eq _ _ _
-#align star_subalgebra.gi StarSubalgebra.gi
+#align star_subalgebra.gi StarAlgebra.gi
 
 theorem adjoin_le {S : StarSubalgebra R A} {s : Set A} (hs : s ⊆ S) : adjoin R s ≤ S :=
-  StarSubalgebra.gc.l_le hs
-#align star_subalgebra.adjoin_le StarSubalgebra.adjoin_le
+  StarAlgebra.gc.l_le hs
+#align star_subalgebra.adjoin_le StarAlgebra.adjoin_le
 
 theorem adjoin_le_iff {S : StarSubalgebra R A} {s : Set A} : adjoin R s ≤ S ↔ s ⊆ S :=
-  StarSubalgebra.gc _ _
-#align star_subalgebra.adjoin_le_iff StarSubalgebra.adjoin_le_iff
+  StarAlgebra.gc _ _
+#align star_subalgebra.adjoin_le_iff StarAlgebra.adjoin_le_iff
 
 theorem _root_.Subalgebra.starClosure_eq_adjoin (S : Subalgebra R A) :
     S.starClosure = adjoin R (S : Set A) :=
@@ -496,7 +498,7 @@ theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin
   Algebra.adjoin_induction h
     (fun x hx => hx.elim (fun hx => mem x hx) fun hx => star_star x ▸ star _ (mem _ hx))
     algebraMap add mul
-#align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_induction
+#align star_subalgebra.adjoin_induction StarAlgebra.adjoin_induction
 
 @[elab_as_elim]
 theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a ∈ adjoin R s)
@@ -524,7 +526,7 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
   · cases' hx with hx hx
     · exact Halg_right _ _ hx
     · exact star_star x ▸ Hstar_left _ _ (Halg_right r _ hx)
-#align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂
+#align star_subalgebra.adjoin_induction₂ StarAlgebra.adjoin_induction₂
 
 /-- The difference with `StarSubalgebra.adjoin_induction` is that this acts on the subtype. -/
 @[elab_as_elim]
@@ -541,7 +543,7 @@ theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
       fun x y hx hy =>
       Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨mul_mem hx' hy', mul _ _ hx hy⟩,
       fun x hx => Exists.elim hx fun hx' hx => ⟨star_mem hx', star _ hx⟩]
-#align star_subalgebra.adjoin_induction' StarSubalgebra.adjoin_induction'
+#align star_subalgebra.adjoin_induction' StarAlgebra.adjoin_induction'
 
 variable (R)
 
@@ -567,7 +569,7 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
             · exact star_star a ▸ (hcomm_star _ hb _ ha).symm
             · simpa only [star_mul, star_star] using congr_arg star (hcomm _ hb _ ha))
       exact congr_arg Subtype.val (mul_comm (⟨x, hx⟩ : Algebra.adjoin R (s ∪ star s)) ⟨y, hy⟩) }
-#align star_subalgebra.adjoin_comm_semiring_of_comm StarSubalgebra.adjoinCommSemiringOfComm
+#align star_subalgebra.adjoin_comm_semiring_of_comm StarAlgebra.adjoinCommSemiringOfComm
 
 /-- If all elements of `s : Set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `StarSubalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
@@ -577,9 +579,9 @@ def adjoinCommRingOfComm (R : Type u) {A : Type v} [CommRing R] [StarRing R] [Ri
     (hcomm : ∀ a : A, a ∈ s → ∀ b : A, b ∈ s → a * b = b * a)
     (hcomm_star : ∀ a : A, a ∈ s → ∀ b : A, b ∈ s → a * star b = star b * a) :
     CommRing (adjoin R s) :=
-  { StarSubalgebra.adjoinCommSemiringOfComm R hcomm hcomm_star,
+  { StarAlgebra.adjoinCommSemiringOfComm R hcomm hcomm_star,
     (adjoin R s).toSubalgebra.toRing with }
-#align star_subalgebra.adjoin_comm_ring_of_comm StarSubalgebra.adjoinCommRingOfComm
+#align star_subalgebra.adjoin_comm_ring_of_comm StarAlgebra.adjoinCommRingOfComm
 
 /-- The star subalgebra `StarSubalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
@@ -592,7 +594,7 @@ instance adjoinCommSemiringOfIsStarNormal (x : A) [IsStarNormal x] :
     fun a ha b hb => by
     rw [Set.mem_singleton_iff] at ha hb
     simpa only [ha, hb] using (star_comm_self' x).symm
-#align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarSubalgebra.adjoinCommSemiringOfIsStarNormal
+#align star_subalgebra.adjoin_comm_semiring_of_is_star_normal StarAlgebra.adjoinCommSemiringOfIsStarNormal
 
 /-- The star subalgebra `StarSubalgebra.adjoin R {x}` generated by a single `x : A` is commutative
 if `x` is normal. -/
@@ -600,15 +602,22 @@ instance adjoinCommRingOfIsStarNormal (R : Type u) {A : Type v} [CommRing R] [St
     [Algebra R A] [StarRing A] [StarModule R A] (x : A) [IsStarNormal x] :
     CommRing (adjoin R ({x} : Set A)) :=
   { (adjoin R ({x} : Set A)).toSubalgebra.toRing with mul_comm := mul_comm }
-#align star_subalgebra.adjoin_comm_ring_of_is_star_normal StarSubalgebra.adjoinCommRingOfIsStarNormal
+#align star_subalgebra.adjoin_comm_ring_of_is_star_normal StarAlgebra.adjoinCommRingOfIsStarNormal
 
 /-! ### Complete lattice structure -/
 
+end StarAlgebra
 
-variable {R} -- Porting note: redundant binder annotation update
+namespace StarSubalgebra
+
+variable {F R A B : Type*} [CommSemiring R] [StarRing R]
+
+variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
+
+variable [Semiring B] [Algebra R B] [StarRing B] [StarModule R B]
 
 instance completeLattice : CompleteLattice (StarSubalgebra R A) where
-  __ := GaloisInsertion.liftCompleteLattice StarSubalgebra.gi
+  __ := GaloisInsertion.liftCompleteLattice StarAlgebra.gi
   bot := { toSubalgebra := ⊥, star_mem' := fun ⟨r, hr⟩ => ⟨star r, hr ▸ algebraMap_star_comm _⟩ }
   bot_le S := (bot_le : ⊥ ≤ S.toSubalgebra)
 
@@ -718,7 +727,7 @@ end StarSubalgebra
 
 namespace StarAlgHom
 
-open StarSubalgebra
+open StarSubalgebra StarAlgebra
 
 variable {F R A B : Type*} [CommSemiring R] [StarRing R]
 variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
@@ -747,8 +756,8 @@ theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (h
 
 theorem map_adjoin (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
-  GaloisConnection.l_comm_of_u_comm Set.image_preimage (gc_map_comap f) StarSubalgebra.gc
-    StarSubalgebra.gc fun _ => rfl
+  GaloisConnection.l_comm_of_u_comm Set.image_preimage (gc_map_comap f) StarAlgebra.gc
+    StarAlgebra.gc fun _ => rfl
 #align star_alg_hom.map_adjoin StarAlgHom.map_adjoin
 
 theorem ext_adjoin {s : Set A} [FunLike F (adjoin R s) B]

I removed some redundant instance arguments throughout Mathlib. To do this, I used VS Code's regex search. See https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/repeating.20instances.20from.20variable.20command I closed the previous PR for this and reopened it.

@@ -745,7 +745,7 @@ theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (h
   DFunLike.ext f g fun _x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
 #align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_top
 
-theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
+theorem map_adjoin (f : A →⋆ₐ[R] B) (s : Set A) :
     map f (adjoin R s) = adjoin R (f '' s) :=
   GaloisConnection.l_comm_of_u_comm Set.image_preimage (gc_map_comap f) StarSubalgebra.gc
     StarSubalgebra.gc fun _ => rfl

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)

@@ -37,11 +37,8 @@ namespace StarSubalgebra
 add_decl_doc StarSubalgebra.toSubalgebra
 
 variable {F R A B C : Type*} [CommSemiring R] [StarRing R]
-
 variable [Semiring A] [StarRing A] [Algebra R A] [StarModule R A]
-
 variable [Semiring B] [StarRing B] [Algebra R B] [StarModule R B]
-
 variable [Semiring C] [StarRing C] [Algebra R C] [StarModule R C]
 
 instance setLike : SetLike (StarSubalgebra R A) A where
@@ -331,9 +328,7 @@ namespace Subalgebra
 open Pointwise
 
 variable {F R A B : Type*} [CommSemiring R] [StarRing R]
-
 variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
-
 variable [Semiring B] [Algebra R B] [StarRing B] [StarModule R B]
 
 /-- The pointwise `star` of a subalgebra is a subalgebra. -/
@@ -418,11 +413,8 @@ end Subalgebra
 namespace StarSubalgebra
 
 variable {F R A B : Type*} [CommSemiring R] [StarRing R]
-
 variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
-
 variable [Semiring B] [Algebra R B] [StarRing B] [StarModule R B]
-
 variable (R)
 
 /-- The minimal star subalgebra that contains `s`. -/
@@ -729,11 +721,8 @@ namespace StarAlgHom
 open StarSubalgebra
 
 variable {F R A B : Type*} [CommSemiring R] [StarRing R]
-
 variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
-
 variable [Semiring B] [Algebra R B] [StarRing B] [StarModule R B]
-
 variable [FunLike F A B] [AlgHomClass F R A B] [StarAlgHomClass F R A B] (f g : F)
 
 /-- The equalizer of two star `R`-algebra homomorphisms. -/

These are the case names used by the induction tactic after the with.

This replaces H0, H1, Hmul etc with zero, one, mul.

This PR does not touch Submonoid or Subgroup, as to_additive does not know how to rename the argument names. There are ways to work around this, but I'd prefer to leave them to a later PR.

This also leaves the closure_induction₂ variants alone, as renaming the arguments is more work for less gain.

@@ -498,12 +498,12 @@ theorem _root_.Subalgebra.starClosure_eq_adjoin (S : Subalgebra R A) :
 `algebraMap`, addition, multiplication and star operations, then it holds for `a ∈ adjoin R s`. -/
 @[elab_as_elim]
 theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin R s)
-    (Hs : ∀ x : A, x ∈ s → p x) (Halg : ∀ r : R, p (algebraMap R A r))
-    (Hadd : ∀ x y : A, p x → p y → p (x + y)) (Hmul : ∀ x y : A, p x → p y → p (x * y))
-    (Hstar : ∀ x : A, p x → p (star x)) : p a :=
+    (mem : ∀ x : A, x ∈ s → p x) (algebraMap : ∀ r : R, p (algebraMap R A r))
+    (add : ∀ x y : A, p x → p y → p (x + y)) (mul : ∀ x y : A, p x → p y → p (x * y))
+    (star : ∀ x : A, p x → p (star x)) : p a :=
   Algebra.adjoin_induction h
-    (fun x hx => hx.elim (fun hx => Hs x hx) fun hx => star_star x ▸ Hstar _ (Hs _ hx)) Halg Hadd
-    Hmul
+    (fun x hx => hx.elim (fun hx => mem x hx) fun hx => star_star x ▸ star _ (mem _ hx))
+    algebraMap add mul
 #align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_induction
 
 @[elab_as_elim]
@@ -537,18 +537,18 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
 /-- The difference with `StarSubalgebra.adjoin_induction` is that this acts on the subtype. -/
 @[elab_as_elim]
 theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
-    (Hs : ∀ (x) (h : x ∈ s), p ⟨x, subset_adjoin R s h⟩) (Halg : ∀ r, p (algebraMap R _ r))
-    (Hadd : ∀ x y, p x → p y → p (x + y)) (Hmul : ∀ x y, p x → p y → p (x * y))
-    (Hstar : ∀ x, p x → p (star x)) : p a :=
+    (mem : ∀ (x) (h : x ∈ s), p ⟨x, subset_adjoin R s h⟩) (algebraMap : ∀ r, p (algebraMap R _ r))
+    (add : ∀ x y, p x → p y → p (x + y)) (mul : ∀ x y, p x → p y → p (x * y))
+    (star : ∀ x, p x → p (star x)) : p a :=
   Subtype.recOn a fun b hb => by
     refine' Exists.elim _ fun (hb : b ∈ adjoin R s) (hc : p ⟨b, hb⟩) => hc
     refine adjoin_induction hb ?_ ?_ ?_ ?_ ?_
-    exacts [fun x hx => ⟨subset_adjoin R s hx, Hs x hx⟩, fun r =>
-      ⟨StarSubalgebra.algebraMap_mem _ r, Halg r⟩, fun x y hx hy =>
-      Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨add_mem hx' hy', Hadd _ _ hx hy⟩,
+    exacts [fun x hx => ⟨subset_adjoin R s hx, mem x hx⟩, fun r =>
+      ⟨StarSubalgebra.algebraMap_mem _ r, algebraMap r⟩, fun x y hx hy =>
+      Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨add_mem hx' hy', add _ _ hx hy⟩,
       fun x y hx hy =>
-      Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨mul_mem hx' hy', Hmul _ _ hx hy⟩,
-      fun x hx => Exists.elim hx fun hx' hx => ⟨star_mem hx', Hstar _ hx⟩]
+      Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨mul_mem hx' hy', mul _ _ hx hy⟩,
+      fun x hx => Exists.elim hx fun hx' hx => ⟨star_mem hx', star _ hx⟩]
 #align star_subalgebra.adjoin_induction' StarSubalgebra.adjoin_induction'
 
 variable (R)

@@ -496,6 +496,7 @@ theorem _root_.Subalgebra.starClosure_eq_adjoin (S : Subalgebra R A) :
 
 /-- If some predicate holds for all `x ∈ (s : Set A)` and this predicate is closed under the
 `algebraMap`, addition, multiplication and star operations, then it holds for `a ∈ adjoin R s`. -/
+@[elab_as_elim]
 theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin R s)
     (Hs : ∀ x : A, x ∈ s → p x) (Halg : ∀ r : R, p (algebraMap R A r))
     (Hadd : ∀ x y : A, p x → p y → p (x + y)) (Hmul : ∀ x y : A, p x → p y → p (x * y))
@@ -505,6 +506,7 @@ theorem adjoin_induction {s : Set A} {p : A → Prop} {a : A} (h : a ∈ adjoin
     Hmul
 #align star_subalgebra.adjoin_induction StarSubalgebra.adjoin_induction
 
+@[elab_as_elim]
 theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a ∈ adjoin R s)
     (hb : b ∈ adjoin R s) (Hs : ∀ x : A, x ∈ s → ∀ y : A, y ∈ s → p x y)
     (Halg : ∀ r₁ r₂ : R, p (algebraMap R A r₁) (algebraMap R A r₂))
@@ -540,7 +542,7 @@ theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
     (Hstar : ∀ x, p x → p (star x)) : p a :=
   Subtype.recOn a fun b hb => by
     refine' Exists.elim _ fun (hb : b ∈ adjoin R s) (hc : p ⟨b, hb⟩) => hc
-    apply adjoin_induction hb
+    refine adjoin_induction hb ?_ ?_ ?_ ?_ ?_
     exacts [fun x hx => ⟨subset_adjoin R s hx, Hs x hx⟩, fun r =>
       ⟨StarSubalgebra.algebraMap_mem _ r, Halg r⟩, fun x y hx hy =>
       Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨add_mem hx' hy', Hadd _ _ hx hy⟩,

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -696,7 +696,7 @@ theorem coe_iInf {ι : Sort*} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i)
 #align star_subalgebra.coe_infi StarSubalgebra.coe_iInf
 
 theorem mem_iInf {ι : Sort*} {S : ι → StarSubalgebra R A} {x : A} :
-    (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [iInf, mem_sInf, Set.forall_range_iff]
+    (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [iInf, mem_sInf, Set.forall_mem_range]
 #align star_subalgebra.mem_infi StarSubalgebra.mem_iInf
 
 @[simp]

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -121,7 +121,7 @@ equalities. -/
 protected def copy (S : StarSubalgebra R A) (s : Set A) (hs : s = ↑S) : StarSubalgebra R A where
   toSubalgebra := Subalgebra.copy S.toSubalgebra s hs
   star_mem' := @fun a ha => hs ▸ (S.star_mem' (by simpa [hs] using ha) : star a ∈ (S : Set A))
-  -- porting note: the old proof kept crashing Lean
+  -- Porting note: the old proof kept crashing Lean
 #align star_subalgebra.copy StarSubalgebra.copy
 
 @[simp]
@@ -276,7 +276,7 @@ theorem comap_id (S : StarSubalgebra R A) : S.comap (StarAlgHom.id R A) = S :=
 theorem comap_comap (S : StarSubalgebra R C) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ[R] B) :
     (S.comap g).comap f = S.comap (g.comp f) :=
   SetLike.coe_injective <| by exact Set.preimage_preimage
-  -- porting note: the `by exact` trick still works sometimes
+  -- Porting note: the `by exact` trick still works sometimes
 #align star_subalgebra.comap_comap StarSubalgebra.comap_comap
 
 @[simp]
@@ -294,7 +294,7 @@ end Map
 
 section Centralizer
 
-variable (R) -- porting note: redundant binder annotation update
+variable (R) -- Porting note: redundant binder annotation update
 
 /-- The centralizer, or commutant, of the star-closure of a set as a star subalgebra. -/
 def centralizer (s : Set A) : StarSubalgebra R A where
@@ -360,7 +360,7 @@ theorem mem_star_iff (S : Subalgebra R A) (x : A) : x ∈ star S ↔ star x ∈
   Iff.rfl
 #align subalgebra.mem_star_iff Subalgebra.mem_star_iff
 
--- porting note: removed `@[simp]` tag because `simp` can prove this
+-- Porting note: removed `@[simp]` tag because `simp` can prove this
 theorem star_mem_star_iff (S : Subalgebra R A) (x : A) : star x ∈ star S ↔ x ∈ S := by
   simp only [mem_star_iff, star_star]
 #align subalgebra.star_mem_star_iff Subalgebra.star_mem_star_iff
@@ -611,7 +611,7 @@ instance adjoinCommRingOfIsStarNormal (R : Type u) {A : Type v} [CommRing R] [St
 /-! ### Complete lattice structure -/
 
 
-variable {R} -- porting note: redundant binder annotation update
+variable {R} -- Porting note: redundant binder annotation update
 
 instance completeLattice : CompleteLattice (StarSubalgebra R A) where
   __ := GaloisInsertion.liftCompleteLattice StarSubalgebra.gi
@@ -633,7 +633,7 @@ theorem mem_top {x : A} : x ∈ (⊤ : StarSubalgebra R A) :=
 
 @[simp]
 theorem top_toSubalgebra : (⊤ : StarSubalgebra R A).toSubalgebra = ⊤ := by ext; simp
--- porting note: Lean can no longer prove this by `rfl`, it times out
+-- Porting note: Lean can no longer prove this by `rfl`, it times out
 #align star_subalgebra.top_to_subalgebra StarSubalgebra.top_toSubalgebra
 
 @[simp]
@@ -672,7 +672,7 @@ theorem mem_inf {S T : StarSubalgebra R A} {x : A} : x ∈ S ⊓ T ↔ x ∈ S 
 theorem inf_toSubalgebra (S T : StarSubalgebra R A) :
     (S ⊓ T).toSubalgebra = S.toSubalgebra ⊓ T.toSubalgebra := by
   ext; simp
--- porting note: Lean can no longer prove this by `rfl`, it times out
+-- Porting note: Lean can no longer prove this by `rfl`, it times out
 #align star_subalgebra.inf_to_subalgebra StarSubalgebra.inf_toSubalgebra
 
 @[simp, norm_cast]
@@ -738,7 +738,7 @@ variable [FunLike F A B] [AlgHomClass F R A B] [StarAlgHomClass F R A B] (f g :
 def equalizer : StarSubalgebra R A :=
   { toSubalgebra := AlgHom.equalizer (f : A →ₐ[R] B) g
     star_mem' := @fun a (ha : f a = g a) => by simpa only [← map_star] using congrArg star ha }
--- porting note: much like `StarSubalgebra.copy` the old proof was broken and hard to fix
+-- Porting note: much like `StarSubalgebra.copy` the old proof was broken and hard to fix
 #align star_alg_hom.equalizer StarAlgHom.equalizer
 
 @[simp]

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.

@@ -533,6 +533,7 @@ theorem adjoin_induction₂ {s : Set A} {p : A → A → Prop} {a b : A} (ha : a
 #align star_subalgebra.adjoin_induction₂ StarSubalgebra.adjoin_induction₂
 
 /-- The difference with `StarSubalgebra.adjoin_induction` is that this acts on the subtype. -/
+@[elab_as_elim]
 theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
     (Hs : ∀ (x) (h : x ∈ s), p ⟨x, subset_adjoin R s h⟩) (Halg : ∀ r, p (algebraMap R _ r))
     (Hadd : ∀ x y, p x → p y → p (x + y)) (Hmul : ∀ x y, p x → p y → p (x * y))

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

@@ -445,7 +445,7 @@ theorem adjoin_toSubalgebra (s : Set A) :
   rfl
 #align star_subalgebra.adjoin_to_subalgebra StarSubalgebra.adjoin_toSubalgebra
 
-@[aesop safe 20 apply (rule_sets [SetLike])]
+@[aesop safe 20 apply (rule_sets := [SetLike])]
 theorem subset_adjoin (s : Set A) : s ⊆ adjoin R s :=
   (Set.subset_union_left s (star s)).trans Algebra.subset_adjoin
 #align star_subalgebra.subset_adjoin StarSubalgebra.subset_adjoin

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -79,7 +79,7 @@ instance algebra (s : StarSubalgebra R A) : Algebra R s :=
 instance starModule (s : StarSubalgebra R A) : StarModule R s where
   star_smul r a := Subtype.ext (star_smul r (a : A))
 
-@[simp, nolint simpNF] -- porting note: `simpNF` says `simp` can prove this, but it can't
+@[simp, nolint simpNF] -- porting note (#10618): `simpNF` says `simp` can prove this, but it can't
 theorem mem_carrier {s : StarSubalgebra R A} {x : A} : x ∈ s.carrier ↔ x ∈ s :=
   Iff.rfl
 #align star_subalgebra.mem_carrier StarSubalgebra.mem_carrier

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>

@@ -731,7 +731,7 @@ variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
 
 variable [Semiring B] [Algebra R B] [StarRing B] [StarModule R B]
 
-variable [hF : StarAlgHomClass F R A B] (f g : F)
+variable [FunLike F A B] [AlgHomClass F R A B] [StarAlgHomClass F R A B] (f g : F)
 
 /-- The equalizer of two star `R`-algebra homomorphisms. -/
 def equalizer : StarSubalgebra R A :=
@@ -759,7 +759,8 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
     StarSubalgebra.gc fun _ => rfl
 #align star_alg_hom.map_adjoin StarAlgHom.map_adjoin
 
-theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
+theorem ext_adjoin {s : Set A} [FunLike F (adjoin R s) B]
+    [AlgHomClass F R (adjoin R s) B] [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g := by
   refine' DFunLike.ext f g fun a =>
     adjoin_induction' (p := fun y => f y = g y) a (fun x hx => _) (fun r => _)
@@ -771,8 +772,10 @@ theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
   · simp only [map_star, hx]
 #align star_alg_hom.ext_adjoin StarAlgHom.ext_adjoin
 
-theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A)) B] {f g : F}
-    (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) : f = g :=
+theorem ext_adjoin_singleton {a : A} [FunLike F (adjoin R ({a} : Set A)) B]
+    [AlgHomClass F R (adjoin R ({a} : Set A)) B] [StarAlgHomClass F R (adjoin R ({a} : Set A)) B]
+    {f g : F} (h : f ⟨a, self_mem_adjoin_singleton R a⟩ = g ⟨a, self_mem_adjoin_singleton R a⟩) :
+    f = g :=
   ext_adjoin fun x hx =>
     (show x = ⟨a, self_mem_adjoin_singleton R a⟩ from
           Subtype.ext <| Set.mem_singleton_iff.mp hx).symm ▸

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>

@@ -750,7 +750,7 @@ theorem adjoin_le_equalizer {s : Set A} (h : s.EqOn f g) : adjoin R s ≤ StarAl
 #align star_alg_hom.adjoin_le_equalizer StarAlgHom.adjoin_le_equalizer
 
 theorem ext_of_adjoin_eq_top {s : Set A} (h : adjoin R s = ⊤) ⦃f g : F⦄ (hs : s.EqOn f g) : f = g :=
-  FunLike.ext f g fun _x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
+  DFunLike.ext f g fun _x => StarAlgHom.adjoin_le_equalizer f g hs <| h.symm ▸ trivial
 #align star_alg_hom.ext_of_adjoin_eq_top StarAlgHom.ext_of_adjoin_eq_top
 
 theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
@@ -761,7 +761,7 @@ theorem map_adjoin [StarModule R B] (f : A →⋆ₐ[R] B) (s : Set A) :
 
 theorem ext_adjoin {s : Set A} [StarAlgHomClass F R (adjoin R s) B] {f g : F}
     (h : ∀ x : adjoin R s, (x : A) ∈ s → f x = g x) : f = g := by
-  refine' FunLike.ext f g fun a =>
+  refine' DFunLike.ext f g fun a =>
     adjoin_induction' (p := fun y => f y = g y) a (fun x hx => _) (fun r => _)
     (fun x y hx hy => _) (fun x y hx hy => _) fun x hx => _
   · exact h ⟨x, subset_adjoin R s hx⟩ hx
@@ -838,7 +838,7 @@ def StarAlgHom.restrictScalars (f : A →⋆ₐ[S] B) : A →⋆ₐ[R] B where
 theorem StarAlgHom.restrictScalars_injective :
     Function.Injective (StarAlgHom.restrictScalars R : (A →⋆ₐ[S] B) → A →⋆ₐ[R] B) :=
   fun f g h => StarAlgHom.ext fun x =>
-    show f.restrictScalars R x = g.restrictScalars R x from FunLike.congr_fun h x
+    show f.restrictScalars R x = g.restrictScalars R x from DFunLike.congr_fun h x
 
 @[simps]
 def StarAlgEquiv.restrictScalars (f : A ≃⋆ₐ[S] B) : A ≃⋆ₐ[R] B :=
@@ -849,6 +849,6 @@ def StarAlgEquiv.restrictScalars (f : A ≃⋆ₐ[S] B) : A ≃⋆ₐ[R] B :=
 theorem StarAlgEquiv.restrictScalars_injective :
     Function.Injective (StarAlgEquiv.restrictScalars R : (A ≃⋆ₐ[S] B) → A ≃⋆ₐ[R] B) :=
   fun f g h => StarAlgEquiv.ext fun x =>
-    show f.restrictScalars R x = g.restrictScalars R x from FunLike.congr_fun h x
+    show f.restrictScalars R x = g.restrictScalars R x from DFunLike.congr_fun h x
 
 end RestrictScalars

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

@@ -736,7 +736,7 @@ variable [hF : StarAlgHomClass F R A B] (f g : F)
 /-- The equalizer of two star `R`-algebra homomorphisms. -/
 def equalizer : StarSubalgebra R A :=
   { toSubalgebra := AlgHom.equalizer (f : A →ₐ[R] B) g
-    star_mem' := @fun a (ha : f a = g a) => by simpa only [←map_star] using congrArg star ha }
+    star_mem' := @fun a (ha : f a = g a) => by simpa only [← map_star] using congrArg star ha }
 -- porting note: much like `StarSubalgebra.copy` the old proof was broken and hard to fix
 #align star_alg_hom.equalizer StarAlgHom.equalizer
 

And the same thing for StarSubalgebra R A. IntermediateField was already handled in #7957.

As a result, nine (obvious) lemmas are now true by definition.

This slightly adjusts the statement of Algebra.toSubmodule_bot to make it simpler and true by definition; the original statement can be recovered by rewriting by Submodule.one_eq_span, which I've had to add in some downstream proofs.

@@ -612,8 +612,10 @@ instance adjoinCommRingOfIsStarNormal (R : Type u) {A : Type v} [CommRing R] [St
 
 variable {R} -- porting note: redundant binder annotation update
 
-instance completeLattice : CompleteLattice (StarSubalgebra R A) :=
-  GaloisInsertion.liftCompleteLattice StarSubalgebra.gi
+instance completeLattice : CompleteLattice (StarSubalgebra R A) where
+  __ := GaloisInsertion.liftCompleteLattice StarSubalgebra.gi
+  bot := { toSubalgebra := ⊥, star_mem' := fun ⟨r, hr⟩ => ⟨star r, hr ▸ algebraMap_star_comm _⟩ }
+  bot_le S := (bot_le : ⊥ ≤ S.toSubalgebra)
 
 instance inhabited : Inhabited (StarSubalgebra R A) :=
   ⟨⊤⟩
@@ -702,18 +704,14 @@ theorem iInf_toSubalgebra {ι : Sort*} (S : ι → StarSubalgebra R A) :
   SetLike.coe_injective <| by simp
 #align star_subalgebra.infi_to_subalgebra StarSubalgebra.iInf_toSubalgebra
 
-theorem bot_toSubalgebra : (⊥ : StarSubalgebra R A).toSubalgebra = ⊥ := by
-  change Algebra.adjoin R (∅ ∪ star ∅) = Algebra.adjoin R ∅
-  simp
+theorem bot_toSubalgebra : (⊥ : StarSubalgebra R A).toSubalgebra = ⊥ := rfl
 #align star_subalgebra.bot_to_subalgebra StarSubalgebra.bot_toSubalgebra
 
-theorem mem_bot {x : A} : x ∈ (⊥ : StarSubalgebra R A) ↔ x ∈ Set.range (algebraMap R A) := by
-  rw [← mem_toSubalgebra, bot_toSubalgebra, Algebra.mem_bot]
+theorem mem_bot {x : A} : x ∈ (⊥ : StarSubalgebra R A) ↔ x ∈ Set.range (algebraMap R A) := Iff.rfl
 #align star_subalgebra.mem_bot StarSubalgebra.mem_bot
 
 @[simp]
-theorem coe_bot : ((⊥ : StarSubalgebra R A) : Set A) = Set.range (algebraMap R A) := by
-  simp [Set.ext_iff, mem_bot]
+theorem coe_bot : ((⊥ : StarSubalgebra R A) : Set A) = Set.range (algebraMap R A) := rfl
 #align star_subalgebra.coe_bot StarSubalgebra.coe_bot
 
 theorem eq_top_iff {S : StarSubalgebra R A} : S = ⊤ ↔ ∀ x : A, x ∈ S :=

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.

@@ -445,6 +445,7 @@ theorem adjoin_toSubalgebra (s : Set A) :
   rfl
 #align star_subalgebra.adjoin_to_subalgebra StarSubalgebra.adjoin_toSubalgebra
 
+@[aesop safe 20 apply (rule_sets [SetLike])]
 theorem subset_adjoin (s : Set A) : s ⊆ adjoin R s :=
   (Set.subset_union_left s (star s)).trans Algebra.subset_adjoin
 #align star_subalgebra.subset_adjoin StarSubalgebra.subset_adjoin

If S is non-unital subalgebra of a unital R-algebra A, there is a natural map Unitization R S →ₐ[R] A whose range is Algebra.adjoin R (S : Set A). When 1 ∉ S and R is a field, this map is injective, and so we can restrict the codomain to Algebra.adjoin R (S : Set A) and turn it into an AlgEquiv.

We specialize this to the ℕ-unitization of a non-unital subsemiring and its Subsemiring.closure, as well as the ℤ-unitization of a non-unital subring and its Subring.closure. We also extend the above map to a StarAlgHom in the case of NonUnitalStarSubalgebras.

This continues the non-unital-ization of mathlib.

Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com>

@@ -58,6 +58,10 @@ instance subsemiringClass : SubsemiringClass (StarSubalgebra R A) A where
   one_mem {s} := s.one_mem'
   zero_mem {s} := s.zero_mem'
 
+instance smulMemClass : SMulMemClass (StarSubalgebra R A) R A where
+  smul_mem {s} r a (ha : a ∈ s.toSubalgebra) :=
+    (SMulMemClass.smul_mem r ha : r • a ∈ s.toSubalgebra)
+
 instance subringClass {R A} [CommRing R] [StarRing R] [Ring A] [StarRing A] [Algebra R A]
     [StarModule R A] : SubringClass (StarSubalgebra R A) A where
   neg_mem {s a} ha := show -a ∈ s.toSubalgebra from neg_mem ha

This is a step towards making sure that all the codRestrict APIs are similar, but they're still not similar enough in wether they take bundled subobjects/morphisms or subobject/morphism classes.

@@ -792,6 +792,20 @@ protected def codRestrict (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) (hf :
   toAlgHom := AlgHom.codRestrict f.toAlgHom S.toSubalgebra hf
   map_star' := fun x => Subtype.ext (map_star f x)
 
+@[simp]
+theorem coe_codRestrict (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) (hf : ∀ x, f x ∈ S) (x : A) :
+    ↑(f.codRestrict S hf x) = f x :=
+  rfl
+
+@[simp]
+theorem subtype_comp_codRestrict (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B)
+    (hf : ∀ x : A, f x ∈ S) : S.subtype.comp (f.codRestrict S hf) = f :=
+  StarAlgHom.ext <| coe_codRestrict _ S hf
+
+theorem injective_codRestrict (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) (hf : ∀ x : A, f x ∈ S) :
+    Function.Injective (StarAlgHom.codRestrict f S hf) ↔ Function.Injective f :=
+  ⟨fun H _x _y hxy => H <| Subtype.eq hxy, fun H _x _y hxy => H (congr_arg Subtype.val hxy : _)⟩
+
 /-- Restriction of the codomain of a `StarAlgHom` to its range. -/
 def rangeRestrict (f : A →⋆ₐ[R] B) : A →⋆ₐ[R] f.range :=
   StarAlgHom.codRestrict f _ fun x => ⟨x, rfl⟩

The mem_map lemmas were inconsistently either not simp lemmas at all, simp lemmas, or simp lemmas with a lowered priority.

This PR makes them uniformly low priority simp lemmas, and adds a few simp attributes to "better" simp lemmas instead. (However these lemmas are themselves quite inconsistent across different algebraic structures, and I haven't attempted to add missing ones.)

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

@@ -220,6 +220,7 @@ theorem map_map (S : StarSubalgebra R A) (g : B →⋆ₐ[R] C) (f : A →⋆ₐ
   SetLike.coe_injective <| Set.image_image _ _ _
 #align star_subalgebra.map_map StarSubalgebra.map_map
 
+@[simp]
 theorem mem_map {S : StarSubalgebra R A} {f : A →⋆ₐ[R] B} {y : B} :
     y ∈ map f S ↔ ∃ x ∈ S, f x = y :=
   Subsemiring.mem_map

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

This has nice performance benefits.

@@ -36,7 +36,7 @@ namespace StarSubalgebra
 -/
 add_decl_doc StarSubalgebra.toSubalgebra
 
-variable {F R A B C : Type _} [CommSemiring R] [StarRing R]
+variable {F R A B C : Type*} [CommSemiring R] [StarRing R]
 
 variable [Semiring A] [StarRing A] [Algebra R A] [StarModule R A]
 
@@ -325,7 +325,7 @@ namespace Subalgebra
 
 open Pointwise
 
-variable {F R A B : Type _} [CommSemiring R] [StarRing R]
+variable {F R A B : Type*} [CommSemiring R] [StarRing R]
 
 variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
 
@@ -412,7 +412,7 @@ end Subalgebra
 
 namespace StarSubalgebra
 
-variable {F R A B : Type _} [CommSemiring R] [StarRing R]
+variable {F R A B : Type*} [CommSemiring R] [StarRing R]
 
 variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
 
@@ -682,16 +682,16 @@ theorem sInf_toSubalgebra (S : Set (StarSubalgebra R A)) :
 #align star_subalgebra.Inf_to_subalgebra StarSubalgebra.sInf_toSubalgebra
 
 @[simp, norm_cast]
-theorem coe_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
+theorem coe_iInf {ι : Sort*} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
   simp [iInf]
 #align star_subalgebra.coe_infi StarSubalgebra.coe_iInf
 
-theorem mem_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} {x : A} :
+theorem mem_iInf {ι : Sort*} {S : ι → StarSubalgebra R A} {x : A} :
     (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [iInf, mem_sInf, Set.forall_range_iff]
 #align star_subalgebra.mem_infi StarSubalgebra.mem_iInf
 
 @[simp]
-theorem iInf_toSubalgebra {ι : Sort _} (S : ι → StarSubalgebra R A) :
+theorem iInf_toSubalgebra {ι : Sort*} (S : ι → StarSubalgebra R A) :
     (⨅ i, S i).toSubalgebra = ⨅ i, (S i).toSubalgebra :=
   SetLike.coe_injective <| by simp
 #align star_subalgebra.infi_to_subalgebra StarSubalgebra.iInf_toSubalgebra
@@ -721,7 +721,7 @@ namespace StarAlgHom
 
 open StarSubalgebra
 
-variable {F R A B : Type _} [CommSemiring R] [StarRing R]
+variable {F R A B : Type*} [CommSemiring R] [StarRing R]
 
 variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
 
@@ -808,7 +808,7 @@ end StarAlgHom
 
 section RestrictScalars
 
-variable (R : Type _) {S A B : Type _} [CommSemiring R]
+variable (R : Type*) {S A B : Type*} [CommSemiring R]
   [CommSemiring S] [Semiring A] [Semiring B] [Algebra R S] [Algebra S A] [Algebra S B]
   [Algebra R A] [Algebra R B] [IsScalarTower R S A] [IsScalarTower R S B] [Star A] [Star B]
 

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.

@@ -382,14 +382,17 @@ variable {R}
 /-- The `StarSubalgebra` obtained from `S : Subalgebra R A` by taking the smallest subalgebra
 containing both `S` and `star S`. -/
 @[simps!]
-def starClosure (S : Subalgebra R A) : StarSubalgebra R A :=
-  { S ⊔ star S with
-    star_mem' := fun {a} ha => by
-      simp only [Subalgebra.mem_carrier, ← (@Algebra.gi R A _ _ _).l_sup_u _ _] at *
-      rw [← mem_star_iff _ a, star_adjoin_comm, sup_comm]
-      simpa using ha }
+def starClosure (S : Subalgebra R A) : StarSubalgebra R A where
+  toSubalgebra := S ⊔ star S
+  star_mem' := fun {a} ha => by
+    simp only [Subalgebra.mem_carrier, ← (@Algebra.gi R A _ _ _).l_sup_u _ _] at *
+    rw [← mem_star_iff _ a, star_adjoin_comm, sup_comm]
+    simpa using ha
 #align subalgebra.star_closure Subalgebra.starClosure
 
+theorem starClosure_toSubalgebra (S : Subalgebra R A) : S.starClosure.toSubalgebra = S ⊔ star S :=
+  rfl
+
 theorem starClosure_le {S₁ : Subalgebra R A} {S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂.toSubalgebra) :
     S₁.starClosure ≤ S₂ :=
   StarSubalgebra.toSubalgebra_le_iff.1 <|

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Jireh Loreaux
-
-! This file was ported from Lean 3 source module algebra.star.subalgebra
-! leanprover-community/mathlib commit 160ef3e338a2a4f21a280e4c152d4016156e516d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Star.Center
 import Mathlib.Algebra.Star.StarAlgHom
@@ -15,6 +10,8 @@ import Mathlib.Algebra.Star.Pointwise
 import Mathlib.Algebra.Star.Module
 import Mathlib.RingTheory.Adjoin.Basic
 
+#align_import algebra.star.subalgebra from "leanprover-community/mathlib"@"160ef3e338a2a4f21a280e4c152d4016156e516d"
+
 /-!
 # Star subalgebras
 

This continues the non-unital-ization of mathlib

This PR also redefines StarSubalgebra.centralizer so that it no longer requires the set s provided to be closed under star, and instead the carrier is just the Set.centralizer (s ∪ star s). Consequently, this changes some things in von Neumann algebras, where we now need to see that Set.centralizer (↑S ∪ star ↑S) = Set.centralizer ↑S, where S is a StarSubalgebra. Therefore we add the simp lemma StarMemClass.star_coe_eq.

• depends on: #5151
• depends on: #5512

@@ -8,6 +8,7 @@ Authors: Scott Morrison, Jireh Loreaux
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathlib.Algebra.Star.Center
 import Mathlib.Algebra.Star.StarAlgHom
 import Mathlib.Algebra.Algebra.Subalgebra.Basic
 import Mathlib.Algebra.Star.Pointwise
@@ -66,7 +67,7 @@ instance subringClass {R A} [CommRing R] [StarRing R] [Ring A] [StarRing A] [Alg
 
 -- this uses the `Star` instance `s` inherits from `StarMemClass (StarSubalgebra R A) A`
 instance starRing (s : StarSubalgebra R A) : StarRing s :=
-  { StarMemClass.star s with
+  { StarMemClass.instStar s with
     star_involutive := fun r => Subtype.ext (star_star (r : A))
     star_mul := fun r₁ r₂ => Subtype.ext (star_mul (r₁ : A) (r₂ : A))
     star_add := fun r₁ r₂ => Subtype.ext (star_add (r₁ : A) (r₂ : A)) }
@@ -87,6 +88,9 @@ theorem ext {S T : StarSubalgebra R A} (h : ∀ x : A, x ∈ S ↔ x ∈ T) : S
   SetLike.ext h
 #align star_subalgebra.ext StarSubalgebra.ext
 
+@[simp]
+lemma coe_mk (S : Subalgebra R A) (h) : ((⟨S, h⟩ : StarSubalgebra R A) : Set A) = S := rfl
+
 @[simp]
 theorem mem_toSubalgebra {S : StarSubalgebra R A} {x} : x ∈ S.toSubalgebra ↔ x ∈ S :=
   Iff.rfl
@@ -290,31 +294,27 @@ section Centralizer
 
 variable (R) -- porting note: redundant binder annotation update
 
-theorem _root_.Set.star_mem_centralizer {a : A} {s : Set A} (h : ∀ a : A, a ∈ s → star a ∈ s)
-    (ha : a ∈ Set.centralizer s) : star a ∈ Set.centralizer s := fun y hy => by
-  simpa using congr_arg star (ha _ (h _ hy)).symm
-#align set.star_mem_centralizer Set.star_mem_centralizer
-
-/-- The centralizer, or commutant, of a *-closed set as star subalgebra. -/
-def centralizer (s : Set A) (w : ∀ a : A, a ∈ s → star a ∈ s) : StarSubalgebra R A :=
-  { Subalgebra.centralizer R s with
-    star_mem' := Set.star_mem_centralizer w }
+/-- The centralizer, or commutant, of the star-closure of a set as a star subalgebra. -/
+def centralizer (s : Set A) : StarSubalgebra R A where
+  toSubalgebra := Subalgebra.centralizer R (s ∪ star s)
+  star_mem' := Set.star_mem_centralizer
 #align star_subalgebra.centralizer StarSubalgebra.centralizer
 
-@[simp]
-theorem coe_centralizer (s : Set A) (w : ∀ a : A, a ∈ s → star a ∈ s) :
-    (centralizer R s w : Set A) = s.centralizer :=
+@[simp, norm_cast]
+theorem coe_centralizer (s : Set A) : (centralizer R s : Set A) = (s ∪ star s).centralizer :=
   rfl
 #align star_subalgebra.coe_centralizer StarSubalgebra.coe_centralizer
 
-theorem mem_centralizer_iff {s : Set A} {w} {z : A} :
-    z ∈ centralizer R s w ↔ ∀ g ∈ s, g * z = z * g :=
-  Iff.rfl
+theorem mem_centralizer_iff {s : Set A} {z : A} :
+    z ∈ centralizer R s ↔ ∀ g ∈ s, g * z = z * g ∧ star g * z = z * star g := by
+  show (∀ g ∈ s ∪ star s, g * z = z * g) ↔ ∀ g ∈ s, g * z = z * g ∧ star g * z = z * star g
+  simp only [Set.mem_union, or_imp, forall_and, and_congr_right_iff]
+  exact fun _ =>
+    ⟨fun hz a ha => hz _ (Set.star_mem_star.mpr ha), fun hz a ha => star_star a ▸ hz _ ha⟩
 #align star_subalgebra.mem_centralizer_iff StarSubalgebra.mem_centralizer_iff
 
-theorem centralizer_le (s t : Set A) (ws : ∀ a : A, a ∈ s → star a ∈ s)
-    (wt : ∀ a : A, a ∈ t → star a ∈ t) (h : s ⊆ t) : centralizer R t wt ≤ centralizer R s ws :=
-  Set.centralizer_subset h
+theorem centralizer_le (s t : Set A) (h : s ⊆ t) : centralizer R t ≤ centralizer R s :=
+  Set.centralizer_subset (Set.union_subset_union h <| Set.preimage_mono h)
 #align star_subalgebra.centralizer_le StarSubalgebra.centralizer_le
 
 end Centralizer

@@ -775,7 +775,7 @@ theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A
       h
 #align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singleton
 
-/-- Range of an `StarAlgHom` as a star subalgebra. -/
+/-- Range of a `StarAlgHom` as a star subalgebra. -/
 protected def range
     (φ : A →⋆ₐ[R] B) : StarSubalgebra R B where
   toSubalgebra := φ.toAlgHom.range

@@ -725,7 +725,7 @@ variable {F R A B : Type _} [CommSemiring R] [StarRing R]
 
 variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
 
-variable [Semiring B] [Algebra R B] [StarRing B]
+variable [Semiring B] [Algebra R B] [StarRing B] [StarModule R B]
 
 variable [hF : StarAlgHomClass F R A B] (f g : F)
 
@@ -775,4 +775,62 @@ theorem ext_adjoin_singleton {a : A} [StarAlgHomClass F R (adjoin R ({a} : Set A
       h
 #align star_alg_hom.ext_adjoin_singleton StarAlgHom.ext_adjoin_singleton
 
+/-- Range of an `StarAlgHom` as a star subalgebra. -/
+protected def range
+    (φ : A →⋆ₐ[R] B) : StarSubalgebra R B where
+  toSubalgebra := φ.toAlgHom.range
+  star_mem' := by rintro _ ⟨b, rfl⟩; exact ⟨star b, map_star φ b⟩
+
+theorem range_eq_map_top (φ : A →⋆ₐ[R] B) : φ.range = (⊤ : StarSubalgebra R A).map φ :=
+  StarSubalgebra.ext fun x =>
+    ⟨by rintro ⟨a, ha⟩; exact ⟨a, by simp, ha⟩, by rintro ⟨a, -, ha⟩; exact ⟨a, ha⟩⟩
+
+/-- Restriction of the codomain of a `StarAlgHom` to a star subalgebra containing the range. -/
+protected def codRestrict (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) (hf : ∀ x, f x ∈ S) :
+    A →⋆ₐ[R] S where
+  toAlgHom := AlgHom.codRestrict f.toAlgHom S.toSubalgebra hf
+  map_star' := fun x => Subtype.ext (map_star f x)
+
+/-- Restriction of the codomain of a `StarAlgHom` to its range. -/
+def rangeRestrict (f : A →⋆ₐ[R] B) : A →⋆ₐ[R] f.range :=
+  StarAlgHom.codRestrict f _ fun x => ⟨x, rfl⟩
+
+/-- The `StarAlgEquiv` onto the range corresponding to an injective `StarAlgHom`. -/
+@[simps]
+noncomputable def _root_.StarAlgEquiv.ofInjective (f : A →⋆ₐ[R] B)
+    (hf : Function.Injective f) : A ≃⋆ₐ[R] f.range :=
+  { AlgEquiv.ofInjective (f : A →ₐ[R] B) hf with
+    toFun := f.rangeRestrict
+    map_star' := fun a => Subtype.ext (map_star f a)
+    map_smul' := fun r a => Subtype.ext (map_smul f r a) }
 end StarAlgHom
+
+
+section RestrictScalars
+
+variable (R : Type _) {S A B : Type _} [CommSemiring R]
+  [CommSemiring S] [Semiring A] [Semiring B] [Algebra R S] [Algebra S A] [Algebra S B]
+  [Algebra R A] [Algebra R B] [IsScalarTower R S A] [IsScalarTower R S B] [Star A] [Star B]
+
+@[simps!]
+def StarAlgHom.restrictScalars (f : A →⋆ₐ[S] B) : A →⋆ₐ[R] B where
+  toAlgHom := f.toAlgHom.restrictScalars R
+  map_star' := map_star f
+
+theorem StarAlgHom.restrictScalars_injective :
+    Function.Injective (StarAlgHom.restrictScalars R : (A →⋆ₐ[S] B) → A →⋆ₐ[R] B) :=
+  fun f g h => StarAlgHom.ext fun x =>
+    show f.restrictScalars R x = g.restrictScalars R x from FunLike.congr_fun h x
+
+@[simps]
+def StarAlgEquiv.restrictScalars (f : A ≃⋆ₐ[S] B) : A ≃⋆ₐ[R] B :=
+  { (f : A →⋆ₐ[S] B).restrictScalars R, f with
+    toFun := f
+    map_smul' := map_smul ((f : A →⋆ₐ[S] B).restrictScalars R) }
+
+theorem StarAlgEquiv.restrictScalars_injective :
+    Function.Injective (StarAlgEquiv.restrictScalars R : (A ≃⋆ₐ[S] B) → A ≃⋆ₐ[R] B) :=
+  fun f g h => StarAlgEquiv.ext fun x =>
+    show f.restrictScalars R x = g.restrictScalars R x from FunLike.congr_fun h x
+
+end RestrictScalars

All of these are doc fixes

@@ -234,7 +234,7 @@ theorem coe_map (S : StarSubalgebra R A) (f : A →⋆ₐ[R] B) : (S.map f : Set
   rfl
 #align star_subalgebra.coe_map StarSubalgebra.coe_map
 
-/-- Preimage of a star subalgebra under an star algebra homomorphism. -/
+/-- Preimage of a star subalgebra under a star algebra homomorphism. -/
 def comap (f : A →⋆ₐ[R] B) (S : StarSubalgebra R B) : StarSubalgebra R A :=
   { S.toSubalgebra.comap f.toAlgHom with
     star_mem' := @fun a ha => show f (star a) ∈ S from (map_star f a).symm ▸ star_mem ha }

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>

@@ -534,7 +534,7 @@ theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
   Subtype.recOn a fun b hb => by
     refine' Exists.elim _ fun (hb : b ∈ adjoin R s) (hc : p ⟨b, hb⟩) => hc
     apply adjoin_induction hb
-    exacts[fun x hx => ⟨subset_adjoin R s hx, Hs x hx⟩, fun r =>
+    exacts [fun x hx => ⟨subset_adjoin R s hx, Hs x hx⟩, fun r =>
       ⟨StarSubalgebra.algebraMap_mem _ r, Halg r⟩, fun x y hx hy =>
       Exists.elim hx fun hx' hx => Exists.elim hy fun hy' hy => ⟨add_mem hx' hy', Hadd _ _ hx hy⟩,
       fun x y hx hy =>

@@ -60,9 +60,6 @@ instance subsemiringClass : SubsemiringClass (StarSubalgebra R A) A where
   one_mem {s} := s.one_mem'
   zero_mem {s} := s.zero_mem'
 
--- porting note: work around lean4#2074
-attribute [-instance] Ring.toNonAssocRing Ring.toNonUnitalRing CommRing.toNonUnitalCommRing
-
 instance subringClass {R A} [CommRing R] [StarRing R] [Ring A] [StarRing A] [Algebra R A]
     [StarModule R A] : SubringClass (StarSubalgebra R A) A where
   neg_mem {s a} ha := show -a ∈ s.toSubalgebra from neg_mem ha
@@ -571,9 +568,6 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
       exact congr_arg Subtype.val (mul_comm (⟨x, hx⟩ : Algebra.adjoin R (s ∪ star s)) ⟨y, hy⟩) }
 #align star_subalgebra.adjoin_comm_semiring_of_comm StarSubalgebra.adjoinCommSemiringOfComm
 
--- porting note: work around lean4#2074
-attribute [-instance] Ring.toNonAssocRing Ring.toNonUnitalRing CommRing.toNonUnitalCommRing
-
 /-- If all elements of `s : Set A` commute pairwise and also commute pairwise with elements of
 `star s`, then `StarSubalgebra.adjoin R s` is commutative. See note [reducible non-instances]. -/
 @[reducible]

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>

@@ -61,7 +61,6 @@ instance subsemiringClass : SubsemiringClass (StarSubalgebra R A) A where
   zero_mem {s} := s.zero_mem'
 
 -- porting note: work around lean4#2074
--- the following instance works with `set_option synthInstance.etaExperiment true`
 attribute [-instance] Ring.toNonAssocRing Ring.toNonUnitalRing CommRing.toNonUnitalCommRing
 
 instance subringClass {R A} [CommRing R] [StarRing R] [Ring A] [StarRing A] [Algebra R A]
@@ -573,7 +572,6 @@ def adjoinCommSemiringOfComm {s : Set A} (hcomm : ∀ a : A, a ∈ s → ∀ b :
 #align star_subalgebra.adjoin_comm_semiring_of_comm StarSubalgebra.adjoinCommSemiringOfComm
 
 -- porting note: work around lean4#2074
--- the following instance works with `set_option synthInstance.etaExperiment true`
 attribute [-instance] Ring.toNonAssocRing Ring.toNonUnitalRing CommRing.toNonUnitalCommRing
 
 /-- If all elements of `s : Set A` commute pairwise and also commute pairwise with elements of

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -675,34 +675,34 @@ theorem inf_toSubalgebra (S T : StarSubalgebra R A) :
 #align star_subalgebra.inf_to_subalgebra StarSubalgebra.inf_toSubalgebra
 
 @[simp, norm_cast]
-theorem coe_infₛ (S : Set (StarSubalgebra R A)) : (↑(infₛ S) : Set A) = ⋂ s ∈ S, ↑s :=
-  infₛ_image
-#align star_subalgebra.coe_Inf StarSubalgebra.coe_infₛ
+theorem coe_sInf (S : Set (StarSubalgebra R A)) : (↑(sInf S) : Set A) = ⋂ s ∈ S, ↑s :=
+  sInf_image
+#align star_subalgebra.coe_Inf StarSubalgebra.coe_sInf
 
-theorem mem_infₛ {S : Set (StarSubalgebra R A)} {x : A} : x ∈ infₛ S ↔ ∀ p ∈ S, x ∈ p := by
-  simp only [← SetLike.mem_coe, coe_infₛ, Set.mem_interᵢ₂]
-#align star_subalgebra.mem_Inf StarSubalgebra.mem_infₛ
+theorem mem_sInf {S : Set (StarSubalgebra R A)} {x : A} : x ∈ sInf S ↔ ∀ p ∈ S, x ∈ p := by
+  simp only [← SetLike.mem_coe, coe_sInf, Set.mem_iInter₂]
+#align star_subalgebra.mem_Inf StarSubalgebra.mem_sInf
 
 @[simp]
-theorem infₛ_toSubalgebra (S : Set (StarSubalgebra R A)) :
-    (infₛ S).toSubalgebra = infₛ (StarSubalgebra.toSubalgebra '' S) :=
+theorem sInf_toSubalgebra (S : Set (StarSubalgebra R A)) :
+    (sInf S).toSubalgebra = sInf (StarSubalgebra.toSubalgebra '' S) :=
   SetLike.coe_injective <| by simp
-#align star_subalgebra.Inf_to_subalgebra StarSubalgebra.infₛ_toSubalgebra
+#align star_subalgebra.Inf_to_subalgebra StarSubalgebra.sInf_toSubalgebra
 
 @[simp, norm_cast]
-theorem coe_infᵢ {ι : Sort _} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
-  simp [infᵢ]
-#align star_subalgebra.coe_infi StarSubalgebra.coe_infᵢ
+theorem coe_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} : (↑(⨅ i, S i) : Set A) = ⋂ i, S i := by
+  simp [iInf]
+#align star_subalgebra.coe_infi StarSubalgebra.coe_iInf
 
-theorem mem_infᵢ {ι : Sort _} {S : ι → StarSubalgebra R A} {x : A} :
-    (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [infᵢ, mem_infₛ, Set.forall_range_iff]
-#align star_subalgebra.mem_infi StarSubalgebra.mem_infᵢ
+theorem mem_iInf {ι : Sort _} {S : ι → StarSubalgebra R A} {x : A} :
+    (x ∈ ⨅ i, S i) ↔ ∀ i, x ∈ S i := by simp only [iInf, mem_sInf, Set.forall_range_iff]
+#align star_subalgebra.mem_infi StarSubalgebra.mem_iInf
 
 @[simp]
-theorem infᵢ_toSubalgebra {ι : Sort _} (S : ι → StarSubalgebra R A) :
+theorem iInf_toSubalgebra {ι : Sort _} (S : ι → StarSubalgebra R A) :
     (⨅ i, S i).toSubalgebra = ⨅ i, (S i).toSubalgebra :=
   SetLike.coe_injective <| by simp
-#align star_subalgebra.infi_to_subalgebra StarSubalgebra.infᵢ_toSubalgebra
+#align star_subalgebra.infi_to_subalgebra StarSubalgebra.iInf_toSubalgebra
 
 theorem bot_toSubalgebra : (⊥ : StarSubalgebra R A).toSubalgebra = ⊥ := by
   change Algebra.adjoin R (∅ ∪ star ∅) = Algebra.adjoin R ∅

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -391,8 +391,7 @@ containing both `S` and `star S`. -/
 @[simps!]
 def starClosure (S : Subalgebra R A) : StarSubalgebra R A :=
   { S ⊔ star S with
-    star_mem' := fun {a} ha =>
-      by
+    star_mem' := fun {a} ha => by
       simp only [Subalgebra.mem_carrier, ← (@Algebra.gi R A _ _ _).l_sup_u _ _] at *
       rw [← mem_star_iff _ a, star_adjoin_comm, sup_comm]
       simpa using ha }
@@ -536,8 +535,7 @@ theorem adjoin_induction' {s : Set A} {p : adjoin R s → Prop} (a : adjoin R s)
     (Hs : ∀ (x) (h : x ∈ s), p ⟨x, subset_adjoin R s h⟩) (Halg : ∀ r, p (algebraMap R _ r))
     (Hadd : ∀ x y, p x → p y → p (x + y)) (Hmul : ∀ x y, p x → p y → p (x * y))
     (Hstar : ∀ x, p x → p (star x)) : p a :=
-  Subtype.recOn a fun b hb =>
-    by
+  Subtype.recOn a fun b hb => by
     refine' Exists.elim _ fun (hb : b ∈ adjoin R s) (hc : p ⟨b, hb⟩) => hc
     apply adjoin_induction hb
     exacts[fun x hx => ⟨subset_adjoin R s hx, Hs x hx⟩, fun r =>

@@ -47,18 +47,18 @@ variable [Semiring B] [StarRing B] [Algebra R B] [StarModule R B]
 variable [Semiring C] [StarRing C] [Algebra R C] [StarModule R C]
 
 instance setLike : SetLike (StarSubalgebra R A) A where
-  coe := fun S ↦ S.carrier
-  coe_injective' := fun p q h => by obtain ⟨⟨⟨⟨⟨_, _⟩, _⟩, _⟩, _⟩, _⟩ := p; cases q; congr
+  coe S := S.carrier
+  coe_injective' p q h := by obtain ⟨⟨⟨⟨⟨_, _⟩, _⟩, _⟩, _⟩, _⟩ := p; cases q; congr
 
 instance starMemClass : StarMemClass (StarSubalgebra R A) A where
-  star_mem := @fun s => s.star_mem'
+  star_mem {s} := s.star_mem'
 
 
 instance subsemiringClass : SubsemiringClass (StarSubalgebra R A) A where
-  add_mem := @fun s => s.add_mem'
-  mul_mem := @fun s => s.mul_mem'
-  one_mem := @fun s => s.one_mem'
-  zero_mem := @fun s => s.zero_mem'
+  add_mem {s} := s.add_mem'
+  mul_mem {s} := s.mul_mem'
+  one_mem {s} := s.one_mem'
+  zero_mem {s} := s.zero_mem'
 
 -- porting note: work around lean4#2074
 -- the following instance works with `set_option synthInstance.etaExperiment true`
@@ -66,11 +66,11 @@ attribute [-instance] Ring.toNonAssocRing Ring.toNonUnitalRing CommRing.toNonUni
 
 instance subringClass {R A} [CommRing R] [StarRing R] [Ring A] [StarRing A] [Algebra R A]
     [StarModule R A] : SubringClass (StarSubalgebra R A) A where
-  neg_mem := @fun s a ha => show -a ∈ s.toSubalgebra from neg_mem ha
+  neg_mem {s a} ha := show -a ∈ s.toSubalgebra from neg_mem ha
 
 -- this uses the `Star` instance `s` inherits from `StarMemClass (StarSubalgebra R A) A`
 instance starRing (s : StarSubalgebra R A) : StarRing s :=
-  { StarMemClass.instStarSubtypeMemInstMembership s with
+  { StarMemClass.star s with
     star_involutive := fun r => Subtype.ext (star_star (r : A))
     star_mul := fun r₁ r₂ => Subtype.ext (star_mul (r₁ : A) (r₂ : A))
     star_add := fun r₁ r₂ => Subtype.ext (star_add (r₁ : A) (r₂ : A)) }
@@ -173,8 +173,7 @@ theorem toSubalgebra_subtype : S.toSubalgebra.val = S.subtype.toAlgHom :=
 
 /-- The inclusion map between `StarSubalgebra`s given by `Subtype.map id` as a `StarAlgHom`. -/
 @[simps]
-def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆ₐ[R] S₂
-    where
+def inclusion {S₁ S₂ : StarSubalgebra R A} (h : S₁ ≤ S₂) : S₁ →⋆ₐ[R] S₂ where
   toFun := Subtype.map id h
   map_one' := rfl
   map_mul' _ _ := rfl
@@ -340,17 +339,14 @@ variable [Semiring A] [Algebra R A] [StarRing A] [StarModule R A]
 variable [Semiring B] [Algebra R B] [StarRing B] [StarModule R B]
 
 /-- The pointwise `star` of a subalgebra is a subalgebra. -/
-instance involutiveStar : InvolutiveStar (Subalgebra R A)
-    where
+instance involutiveStar : InvolutiveStar (Subalgebra R A) where
   star S :=
     { carrier := star S.carrier
-      mul_mem' := @fun x y hx hy =>
-        by
+      mul_mem' := fun {x y} hx hy => by
         simp only [Set.mem_star, Subalgebra.mem_carrier] at *
         exact (star_mul x y).symm ▸ mul_mem hy hx
       one_mem' := Set.mem_star.mp ((star_one A).symm ▸ one_mem S : star (1 : A) ∈ S)
-      add_mem' := @fun x y hx hy =>
-        by
+      add_mem' := fun {x y} hx hy => by
         simp only [Set.mem_star, Subalgebra.mem_carrier] at *
         exact (star_add x y).symm ▸ add_mem hx hy
       zero_mem' := Set.mem_star.mp ((star_zero A).symm ▸ zero_mem S : star (0 : A) ∈ S)
@@ -395,7 +391,7 @@ containing both `S` and `star S`. -/
 @[simps!]
 def starClosure (S : Subalgebra R A) : StarSubalgebra R A :=
   { S ⊔ star S with
-    star_mem' := @fun a ha =>
+    star_mem' := fun {a} ha =>
       by
       simp only [Subalgebra.mem_carrier, ← (@Algebra.gi R A _ _ _).l_sup_u _ _] at *
       rw [← mem_star_iff _ a, star_adjoin_comm, sup_comm]
@@ -433,7 +429,7 @@ variable (R)
 @[simps!]
 def adjoin (s : Set A) : StarSubalgebra R A :=
   { Algebra.adjoin R (s ∪ star s) with
-    star_mem' := @fun x hx => by
+    star_mem' := fun hx => by
       rwa [Subalgebra.mem_carrier, ← Subalgebra.mem_star_iff, Subalgebra.star_adjoin_comm,
         Set.union_star, star_star, Set.union_comm] }
 #align star_subalgebra.adjoin StarSubalgebra.adjoin
@@ -476,8 +472,7 @@ protected theorem gc : GaloisConnection (adjoin R : Set A → StarSubalgebra R A
 #align star_subalgebra.gc StarSubalgebra.gc
 
 /-- Galois insertion between `adjoin` and `coe`. -/
-protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) (↑)
-    where
+protected def gi : GaloisInsertion (adjoin R : Set A → StarSubalgebra R A) (↑) where
   choice s hs := (adjoin R s).copy s <| le_antisymm (StarSubalgebra.gc.le_u_l s) hs
   gc := StarSubalgebra.gc
   le_l_u S := (StarSubalgebra.gc (S : Set A) (adjoin R S)).1 <| le_rfl

Note: Lean was continually crashing on me as I was porting this file, I believe sure to autoparams.

• depends on: #2817