computability.language ⟷ Mathlib.Computability.Language

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Fox Thomson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Fox Thomson
 -/
-import Algebra.Hom.Ring
+import Algebra.Ring.Hom.Defs
 import Algebra.Order.Kleene
 import Data.List.Join
 import Data.Set.Lattice
@@ -293,7 +293,7 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
     constructor
     · rintro rfl; exact ⟨[], rfl, rfl, fun y h => h.elim⟩
     · rintro ⟨_, rfl, rfl, _⟩; rfl
-  · simp only [pow_succ, mem_mul, ihn]
+  · simp only [pow_succ', mem_mul, ihn]
     constructor
     · rintro ⟨a, b, ha, ⟨S, rfl, rfl, hS⟩, rfl⟩
       exact ⟨a :: S, rfl, rfl, forall_mem_cons.2 ⟨ha, hS⟩⟩
@@ -326,7 +326,7 @@ theorem map_kstar (f : α → β) (l : Language α) : map f l∗ = (map f l)∗
 
 #print Language.mul_self_kstar_comm /-
 theorem mul_self_kstar_comm (l : Language α) : l∗ * l = l * l∗ := by
-  simp only [kstar_eq_supr_pow, mul_supr, supr_mul, ← pow_succ, ← pow_succ']
+  simp only [kstar_eq_supr_pow, mul_supr, supr_mul, ← pow_succ', ← pow_succ]
 #align language.mul_self_kstar_comm Language.mul_self_kstar_comm
 -/
 
@@ -334,7 +334,7 @@ theorem mul_self_kstar_comm (l : Language α) : l∗ * l = l * l∗ := by
 @[simp]
 theorem one_add_self_mul_kstar_eq_kstar (l : Language α) : 1 + l * l∗ = l∗ :=
   by
-  simp only [kstar_eq_supr_pow, mul_supr, ← pow_succ, ← pow_zero l]
+  simp only [kstar_eq_supr_pow, mul_supr, ← pow_succ', ← pow_zero l]
   exact sup_iSup_nat_succ _
 #align language.one_add_self_mul_kstar_eq_kstar Language.one_add_self_mul_kstar_eq_kstar
 -/
@@ -358,7 +358,7 @@ instance : KleeneAlgebra (Language α) :=
       refine' iSup_le fun n => _
       induction' n with n ih
       · simp
-      rw [pow_succ', mul_assoc (l ^ n) l m]
+      rw [pow_succ, mul_assoc (l ^ n) l m]
       exact le_trans (le_mul_congr le_rfl h) ih
     mul_kstar_le_self := fun l m h =>
       by
@@ -366,7 +366,7 @@ instance : KleeneAlgebra (Language α) :=
       refine' iSup_le fun n => _
       induction' n with n ih
       · simp
-      rw [pow_succ, ← mul_assoc m l (l ^ n)]
+      rw [pow_succ', ← mul_assoc m l (l ^ n)]
       exact le_trans (le_mul_congr h le_rfl) ih }
 
 end Language

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

@@ -222,7 +222,7 @@ theorem kstar_def_nonempty (l : Language α) :
   constructor
   · rintro ⟨S, rfl, h⟩
     refine' ⟨S.filter fun l => ¬List.isEmpty l, by simp, fun y hy => _⟩
-    rw [mem_filter, empty_iff_eq_nil] at hy 
+    rw [mem_filter, empty_iff_eq_nil] at hy
     exact ⟨h y hy.1, hy.2⟩
   · rintro ⟨S, hx, h⟩
     exact ⟨S, hx, fun y hy => (h y hy).1⟩
@@ -298,7 +298,7 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
     · rintro ⟨a, b, ha, ⟨S, rfl, rfl, hS⟩, rfl⟩
       exact ⟨a :: S, rfl, rfl, forall_mem_cons.2 ⟨ha, hS⟩⟩
     · rintro ⟨_ | ⟨a, S⟩, rfl, hn, hS⟩ <;> cases hn
-      rw [forall_mem_cons] at hS 
+      rw [forall_mem_cons] at hS
       exact ⟨a, _, hS.1, ⟨S, rfl, rfl, hS.2⟩, rfl⟩
 #align language.mem_pow Language.mem_pow
 -/

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

@@ -3,10 +3,10 @@ Copyright (c) 2020 Fox Thomson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Fox Thomson
 -/
-import Mathbin.Algebra.Hom.Ring
-import Mathbin.Algebra.Order.Kleene
-import Mathbin.Data.List.Join
-import Mathbin.Data.Set.Lattice
+import Algebra.Hom.Ring
+import Algebra.Order.Kleene
+import Data.List.Join
+import Data.Set.Lattice
 
 #align_import computability.language from "leanprover-community/mathlib"@"e97cf15cd1aec9bd5c193b2ffac5a6dc9118912b"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Fox Thomson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Fox Thomson
-
-! This file was ported from Lean 3 source module computability.language
-! leanprover-community/mathlib commit e97cf15cd1aec9bd5c193b2ffac5a6dc9118912b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Hom.Ring
 import Mathbin.Algebra.Order.Kleene
 import Mathbin.Data.List.Join
 import Mathbin.Data.Set.Lattice
 
+#align_import computability.language from "leanprover-community/mathlib"@"e97cf15cd1aec9bd5c193b2ffac5a6dc9118912b"
+
 /-!
 # Languages
 

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

@@ -87,9 +87,11 @@ theorem one_def : (1 : Language α) = {[]} :=
 #align language.one_def Language.one_def
 -/
 
+#print Language.add_def /-
 theorem add_def (l m : Language α) : l + m = l ∪ m :=
   rfl
 #align language.add_def Language.add_def
+-/
 
 #print Language.mul_def /-
 theorem mul_def (l m : Language α) : l * m = image2 (· ++ ·) l m :=
@@ -127,9 +129,11 @@ theorem nil_mem_one : [] ∈ (1 : Language α) :=
 #align language.nil_mem_one Language.nil_mem_one
 -/
 
+#print Language.mem_add /-
 theorem mem_add (l m : Language α) (x : List α) : x ∈ l + m ↔ x ∈ l ∨ x ∈ m :=
   Iff.rfl
 #align language.mem_add Language.mem_add
+-/
 
 #print Language.mem_mul /-
 theorem mem_mul : x ∈ l * m ↔ ∃ a b, a ∈ l ∧ b ∈ m ∧ a ++ b = x :=
@@ -181,11 +185,14 @@ instance : Semiring (Language α) where
   left_distrib _ _ _ := image2_union_right
   right_distrib _ _ _ := image2_union_left
 
+#print Language.add_self /-
 @[simp]
 theorem add_self (l : Language α) : l + l = l :=
   sup_idem
 #align language.add_self Language.add_self
+-/
 
+#print Language.map /-
 /-- Maps the alphabet of a language. -/
 def map (f : α → β) : Language α →+* Language β
     where
@@ -195,15 +202,20 @@ def map (f : α → β) : Language α →+* Language β
   map_add' := image_union _
   map_mul' _ _ := image_image2_distrib <| map_append _
 #align language.map Language.map
+-/
 
+#print Language.map_id /-
 @[simp]
 theorem map_id (l : Language α) : map id l = l := by simp [map]
 #align language.map_id Language.map_id
+-/
 
+#print Language.map_map /-
 @[simp]
 theorem map_map (g : β → γ) (f : α → β) (l : Language α) : map g (map f l) = map (g ∘ f) l := by
   simp [map, image_image]
 #align language.map_map Language.map_map
+-/
 
 #print Language.kstar_def_nonempty /-
 theorem kstar_def_nonempty (l : Language α) :
@@ -220,9 +232,11 @@ theorem kstar_def_nonempty (l : Language α) :
 #align language.kstar_def_nonempty Language.kstar_def_nonempty
 -/
 
+#print Language.le_iff /-
 theorem le_iff (l m : Language α) : l ≤ m ↔ l + m = m :=
   sup_eq_right.symm
 #align language.le_iff Language.le_iff
+-/
 
 #print Language.le_mul_congr /-
 theorem le_mul_congr {l₁ l₂ m₁ m₂ : Language α} : l₁ ≤ m₁ → l₂ ≤ m₂ → l₁ * l₂ ≤ m₁ * m₂ :=
@@ -233,34 +247,47 @@ theorem le_mul_congr {l₁ l₂ m₁ m₂ : Language α} : l₁ ≤ m₁ → l
 #align language.le_mul_congr Language.le_mul_congr
 -/
 
+#print Language.le_add_congr /-
 theorem le_add_congr {l₁ l₂ m₁ m₂ : Language α} : l₁ ≤ m₁ → l₂ ≤ m₂ → l₁ + l₂ ≤ m₁ + m₂ :=
   sup_le_sup
 #align language.le_add_congr Language.le_add_congr
+-/
 
+#print Language.mem_iSup /-
 theorem mem_iSup {ι : Sort v} {l : ι → Language α} {x : List α} : (x ∈ ⨆ i, l i) ↔ ∃ i, x ∈ l i :=
   mem_iUnion
 #align language.mem_supr Language.mem_iSup
+-/
 
+#print Language.iSup_mul /-
 theorem iSup_mul {ι : Sort v} (l : ι → Language α) (m : Language α) :
     (⨆ i, l i) * m = ⨆ i, l i * m :=
   image2_iUnion_left _ _ _
 #align language.supr_mul Language.iSup_mul
+-/
 
+#print Language.mul_iSup /-
 theorem mul_iSup {ι : Sort v} (l : ι → Language α) (m : Language α) :
     (m * ⨆ i, l i) = ⨆ i, m * l i :=
   image2_iUnion_right _ _ _
 #align language.mul_supr Language.mul_iSup
+-/
 
+#print Language.iSup_add /-
 theorem iSup_add {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
     (⨆ i, l i) + m = ⨆ i, l i + m :=
   iSup_sup
 #align language.supr_add Language.iSup_add
+-/
 
+#print Language.add_iSup /-
 theorem add_iSup {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
     (m + ⨆ i, l i) = ⨆ i, m + l i :=
   sup_iSup
 #align language.add_supr Language.add_iSup
+-/
 
+#print Language.mem_pow /-
 theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
     x ∈ l ^ n ↔ ∃ S : List (List α), x = S.join ∧ S.length = n ∧ ∀ y ∈ S, y ∈ l :=
   by
@@ -277,7 +304,9 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
       rw [forall_mem_cons] at hS 
       exact ⟨a, _, hS.1, ⟨S, rfl, rfl, hS.2⟩, rfl⟩
 #align language.mem_pow Language.mem_pow
+-/
 
+#print Language.kstar_eq_iSup_pow /-
 theorem kstar_eq_iSup_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
   by
   ext x
@@ -286,7 +315,9 @@ theorem kstar_eq_iSup_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
   · rintro ⟨S, rfl, hS⟩; exact ⟨_, S, rfl, rfl, hS⟩
   · rintro ⟨_, S, rfl, rfl, hS⟩; exact ⟨S, rfl, hS⟩
 #align language.kstar_eq_supr_pow Language.kstar_eq_iSup_pow
+-/
 
+#print Language.map_kstar /-
 @[simp]
 theorem map_kstar (f : α → β) (l : Language α) : map f l∗ = (map f l)∗ :=
   by
@@ -294,6 +325,7 @@ theorem map_kstar (f : α → β) (l : Language α) : map f l∗ = (map f l)∗
   simp_rw [← map_pow]
   exact image_Union
 #align language.map_kstar Language.map_kstar
+-/
 
 #print Language.mul_self_kstar_comm /-
 theorem mul_self_kstar_comm (l : Language α) : l∗ * l = l * l∗ := by
@@ -301,17 +333,21 @@ theorem mul_self_kstar_comm (l : Language α) : l∗ * l = l * l∗ := by
 #align language.mul_self_kstar_comm Language.mul_self_kstar_comm
 -/
 
+#print Language.one_add_self_mul_kstar_eq_kstar /-
 @[simp]
 theorem one_add_self_mul_kstar_eq_kstar (l : Language α) : 1 + l * l∗ = l∗ :=
   by
   simp only [kstar_eq_supr_pow, mul_supr, ← pow_succ, ← pow_zero l]
   exact sup_iSup_nat_succ _
 #align language.one_add_self_mul_kstar_eq_kstar Language.one_add_self_mul_kstar_eq_kstar
+-/
 
+#print Language.one_add_kstar_mul_self_eq_kstar /-
 @[simp]
 theorem one_add_kstar_mul_self_eq_kstar (l : Language α) : 1 + l∗ * l = l∗ := by
   rw [mul_self_kstar_comm, one_add_self_mul_kstar_eq_kstar]
 #align language.one_add_kstar_mul_self_eq_kstar Language.one_add_kstar_mul_self_eq_kstar
+-/
 
 instance : KleeneAlgebra (Language α) :=
   { Language.semiring, Set.completeBooleanAlgebra,

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

@@ -34,17 +34,17 @@ universe v
 
 variable {α β γ : Type _}
 
-/- ./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler has_mem[has_mem] (list[list] α) -/
-/- ./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler has_singleton[has_singleton] (list[list] α) -/
-/- ./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler has_insert[has_insert] (list[list] α) -/
+/- ./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler has_mem[has_mem] (list[list] α) -/
+/- ./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler has_singleton[has_singleton] (list[list] α) -/
+/- ./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler has_insert[has_insert] (list[list] α) -/
 #print Language /-
 /-- A language is a set of strings over an alphabet. -/
 def Language (α) :=
   Set (List α)
 deriving
-  «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler has_mem[has_mem] (list[list] α)»,
-  «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler has_singleton[has_singleton] (list[list] α)»,
-  «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler has_insert[has_insert] (list[list] α)»,
+  «./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler has_mem[has_mem] (list[list] α)»,
+  «./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler has_singleton[has_singleton] (list[list] α)»,
+  «./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler has_insert[has_insert] (list[list] α)»,
   CompleteBooleanAlgebra
 #align language Language
 -/
@@ -100,11 +100,10 @@ theorem mul_def (l m : Language α) : l * m = image2 (· ++ ·) l m :=
 /-- The Kleene star of a language `L` is the set of all strings which can be written by
 concatenating strings from `L`. -/
 instance : KStar (Language α) :=
-  ⟨fun l => { x | ∃ L : List (List α), x = L.join ∧ ∀ y ∈ L, y ∈ l }⟩
+  ⟨fun l => {x | ∃ L : List (List α), x = L.join ∧ ∀ y ∈ L, y ∈ l}⟩
 
 #print Language.kstar_def /-
-theorem kstar_def (l : Language α) :
-    l∗ = { x | ∃ L : List (List α), x = L.join ∧ ∀ y ∈ L, y ∈ l } :=
+theorem kstar_def (l : Language α) : l∗ = {x | ∃ L : List (List α), x = L.join ∧ ∀ y ∈ L, y ∈ l} :=
   rfl
 #align language.kstar_def Language.kstar_def
 -/
@@ -208,7 +207,7 @@ theorem map_map (g : β → γ) (f : α → β) (l : Language α) : map g (map f
 
 #print Language.kstar_def_nonempty /-
 theorem kstar_def_nonempty (l : Language α) :
-    l∗ = { x | ∃ S : List (List α), x = S.join ∧ ∀ y ∈ S, y ∈ l ∧ y ≠ [] } :=
+    l∗ = {x | ∃ S : List (List α), x = S.join ∧ ∀ y ∈ S, y ∈ l ∧ y ≠ []} :=
   by
   ext x
   constructor

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

@@ -40,7 +40,8 @@ variable {α β γ : Type _}
 #print Language /-
 /-- A language is a set of strings over an alphabet. -/
 def Language (α) :=
-  Set (List α)deriving
+  Set (List α)
+deriving
   «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler has_mem[has_mem] (list[list] α)»,
   «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler has_singleton[has_singleton] (list[list] α)»,
   «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler has_insert[has_insert] (list[list] α)»,
@@ -213,7 +214,7 @@ theorem kstar_def_nonempty (l : Language α) :
   constructor
   · rintro ⟨S, rfl, h⟩
     refine' ⟨S.filter fun l => ¬List.isEmpty l, by simp, fun y hy => _⟩
-    rw [mem_filter, empty_iff_eq_nil] at hy
+    rw [mem_filter, empty_iff_eq_nil] at hy 
     exact ⟨h y hy.1, hy.2⟩
   · rintro ⟨S, hx, h⟩
     exact ⟨S, hx, fun y hy => (h y hy).1⟩
@@ -228,7 +229,7 @@ theorem le_iff (l m : Language α) : l ≤ m ↔ l + m = m :=
 theorem le_mul_congr {l₁ l₂ m₁ m₂ : Language α} : l₁ ≤ m₁ → l₂ ≤ m₂ → l₁ * l₂ ≤ m₁ * m₂ :=
   by
   intro h₁ h₂ x hx
-  simp only [mul_def, exists_and_left, mem_image2, image_prod] at hx⊢
+  simp only [mul_def, exists_and_left, mem_image2, image_prod] at hx ⊢
   tauto
 #align language.le_mul_congr Language.le_mul_congr
 -/
@@ -274,7 +275,7 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
     · rintro ⟨a, b, ha, ⟨S, rfl, rfl, hS⟩, rfl⟩
       exact ⟨a :: S, rfl, rfl, forall_mem_cons.2 ⟨ha, hS⟩⟩
     · rintro ⟨_ | ⟨a, S⟩, rfl, hn, hS⟩ <;> cases hn
-      rw [forall_mem_cons] at hS
+      rw [forall_mem_cons] at hS 
       exact ⟨a, _, hS.1, ⟨S, rfl, rfl, hS.2⟩, rfl⟩
 #align language.mem_pow Language.mem_pow
 

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

@@ -28,7 +28,7 @@ over the languages.
 
 open List Set
 
-open Computability
+open scoped Computability
 
 universe v
 

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

@@ -86,12 +86,6 @@ theorem one_def : (1 : Language α) = {[]} :=
 #align language.one_def Language.one_def
 -/
 
-/- warning: language.add_def -> Language.add_def is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (l : Language.{u1} α) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.hasAdd.{u1} α)) l m) (Union.union.{u1} (Language.{u1} α) (Set.hasUnion.{u1} (List.{u1} α)) l m)
-but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) l m) (Union.union.{u1} (Set.{u1} (List.{u1} α)) (Set.instUnionSet.{u1} (List.{u1} α)) l m)
-Case conversion may be inaccurate. Consider using '#align language.add_def Language.add_defₓ'. -/
 theorem add_def (l m : Language α) : l + m = l ∪ m :=
   rfl
 #align language.add_def Language.add_def
@@ -133,12 +127,6 @@ theorem nil_mem_one : [] ∈ (1 : Language α) :=
 #align language.nil_mem_one Language.nil_mem_one
 -/
 
-/- warning: language.mem_add -> Language.mem_add is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (l : Language.{u1} α) (m : Language.{u1} α) (x : List.{u1} α), Iff (Membership.Mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (Language.hasMem.{u1} α) x (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.hasAdd.{u1} α)) l m)) (Or (Membership.Mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (Language.hasMem.{u1} α) x l) (Membership.Mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (Language.hasMem.{u1} α) x m))
-but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α) (m : Language.{u1} α) (x : List.{u1} α), Iff (Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) l m)) (Or (Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x l) (Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x m))
-Case conversion may be inaccurate. Consider using '#align language.mem_add Language.mem_addₓ'. -/
 theorem mem_add (l m : Language α) (x : List α) : x ∈ l + m ↔ x ∈ l ∨ x ∈ m :=
   Iff.rfl
 #align language.mem_add Language.mem_add
@@ -193,23 +181,11 @@ instance : Semiring (Language α) where
   left_distrib _ _ _ := image2_union_right
   right_distrib _ _ _ := image2_union_left
 
-/- warning: language.add_self -> Language.add_self is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.hasAdd.{u1} α)) l l) l
-but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) l l) l
-Case conversion may be inaccurate. Consider using '#align language.add_self Language.add_selfₓ'. -/
 @[simp]
 theorem add_self (l : Language α) : l + l = l :=
   sup_idem
 #align language.add_self Language.add_self
 
-/- warning: language.map -> Language.map is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}}, (α -> β) -> (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}}, (α -> β) -> (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.instSemiringLanguage.{u2} β)))
-Case conversion may be inaccurate. Consider using '#align language.map Language.mapₓ'. -/
 /-- Maps the alphabet of a language. -/
 def map (f : α → β) : Language α →+* Language β
     where
@@ -220,19 +196,10 @@ def map (f : α → β) : Language α →+* Language β
   map_mul' _ _ := image_image2_distrib <| map_append _
 #align language.map Language.map
 
-/- warning: language.map_id -> Language.map_id is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) (fun (_x : RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) => (Language.{u1} α) -> (Language.{u1} α)) (RingHom.hasCoeToFun.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
-but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u1} α) => Language.{u1} α) l) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (fun (_x : Language.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u1} α) => Language.{u1} α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (RingHom.instRingHomClassRingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
-Case conversion may be inaccurate. Consider using '#align language.map_id Language.map_idₓ'. -/
 @[simp]
 theorem map_id (l : Language α) : map id l = l := by simp [map]
 #align language.map_id Language.map_id
 
-/- warning: language.map_map -> Language.map_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align language.map_map Language.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β → γ) (f : α → β) (l : Language α) : map g (map f l) = map (g ∘ f) l := by
   simp [map, image_image]
@@ -253,12 +220,6 @@ theorem kstar_def_nonempty (l : Language α) :
 #align language.kstar_def_nonempty Language.kstar_def_nonempty
 -/
 
-/- warning: language.le_iff -> Language.le_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (l : Language.{u1} α) (m : Language.{u1} α), Iff (LE.le.{u1} (Language.{u1} α) (Set.hasLe.{u1} (List.{u1} α)) l m) (Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.hasAdd.{u1} α)) l m) m)
-but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α) (m : Language.{u1} α), Iff (LE.le.{u1} (Language.{u1} α) (Preorder.toLE.{u1} (Language.{u1} α) (PartialOrder.toPreorder.{u1} (Language.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Language.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Language.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Language.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Language.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)))))))) l m) (Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) l m) m)
-Case conversion may be inaccurate. Consider using '#align language.le_iff Language.le_iffₓ'. -/
 theorem le_iff (l m : Language α) : l ≤ m ↔ l + m = m :=
   sup_eq_right.symm
 #align language.le_iff Language.le_iff
@@ -272,76 +233,34 @@ theorem le_mul_congr {l₁ l₂ m₁ m₂ : Language α} : l₁ ≤ m₁ → l
 #align language.le_mul_congr Language.le_mul_congr
 -/
 
-/- warning: language.le_add_congr -> Language.le_add_congr is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {l₁ : Language.{u1} α} {l₂ : Language.{u1} α} {m₁ : Language.{u1} α} {m₂ : Language.{u1} α}, (LE.le.{u1} (Language.{u1} α) (Set.hasLe.{u1} (List.{u1} α)) l₁ m₁) -> (LE.le.{u1} (Language.{u1} α) (Set.hasLe.{u1} (List.{u1} α)) l₂ m₂) -> (LE.le.{u1} (Language.{u1} α) (Set.hasLe.{u1} (List.{u1} α)) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.hasAdd.{u1} α)) l₁ l₂) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.hasAdd.{u1} α)) m₁ m₂))
-but is expected to have type
-  forall {α : Type.{u1}} {l₁ : Language.{u1} α} {l₂ : Language.{u1} α} {m₁ : Language.{u1} α} {m₂ : Language.{u1} α}, (LE.le.{u1} (Language.{u1} α) (Preorder.toLE.{u1} (Language.{u1} α) (PartialOrder.toPreorder.{u1} (Language.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Language.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Language.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Language.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Language.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)))))))) l₁ m₁) -> (LE.le.{u1} (Language.{u1} α) (Preorder.toLE.{u1} (Language.{u1} α) (PartialOrder.toPreorder.{u1} (Language.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Language.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Language.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Language.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Language.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)))))))) l₂ m₂) -> (LE.le.{u1} (Language.{u1} α) (Preorder.toLE.{u1} (Language.{u1} α) (PartialOrder.toPreorder.{u1} (Language.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Language.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Language.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Language.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Language.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)))))))) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) l₁ l₂) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) m₁ m₂))
-Case conversion may be inaccurate. Consider using '#align language.le_add_congr Language.le_add_congrₓ'. -/
 theorem le_add_congr {l₁ l₂ m₁ m₂ : Language α} : l₁ ≤ m₁ → l₂ ≤ m₂ → l₁ + l₂ ≤ m₁ + m₂ :=
   sup_le_sup
 #align language.le_add_congr Language.le_add_congr
 
-/- warning: language.mem_supr -> Language.mem_iSup is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} {l : ι -> (Language.{u2} α)} {x : List.{u2} α}, Iff (Membership.Mem.{u2, u2} (List.{u2} α) (Language.{u2} α) (Language.hasMem.{u2} α) x (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i))) (Exists.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} (List.{u2} α) (Language.{u2} α) (Language.hasMem.{u2} α) x (l i)))
-but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {l : ι -> (Language.{u1} α)} {x : List.{u1} α}, Iff (Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i))) (Exists.{u2} ι (fun (i : ι) => Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x (l i)))
-Case conversion may be inaccurate. Consider using '#align language.mem_supr Language.mem_iSupₓ'. -/
 theorem mem_iSup {ι : Sort v} {l : ι → Language α} {x : List α} : (x ∈ ⨆ i, l i) ↔ ∃ i, x ∈ l i :=
   mem_iUnion
 #align language.mem_supr Language.mem_iSup
 
-/- warning: language.supr_mul -> Language.iSup_mul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i)) m) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) (l i) m))
-but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i)) m) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) (l i) m))
-Case conversion may be inaccurate. Consider using '#align language.supr_mul Language.iSup_mulₓ'. -/
 theorem iSup_mul {ι : Sort v} (l : ι → Language α) (m : Language α) :
     (⨆ i, l i) * m = ⨆ i, l i * m :=
   image2_iUnion_left _ _ _
 #align language.supr_mul Language.iSup_mul
 
-/- warning: language.mul_supr -> Language.mul_iSup is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) m (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i))) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) m (l i)))
-but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) m (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i))) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) m (l i)))
-Case conversion may be inaccurate. Consider using '#align language.mul_supr Language.mul_iSupₓ'. -/
 theorem mul_iSup {ι : Sort v} (l : ι → Language α) (m : Language α) :
     (m * ⨆ i, l i) = ⨆ i, m * l i :=
   image2_iUnion_right _ _ _
 #align language.mul_supr Language.mul_iSup
 
-/- warning: language.supr_add -> Language.iSup_add is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i)) m) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) (l i) m))
-but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i)) m) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) (l i) m))
-Case conversion may be inaccurate. Consider using '#align language.supr_add Language.iSup_addₓ'. -/
 theorem iSup_add {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
     (⨆ i, l i) + m = ⨆ i, l i + m :=
   iSup_sup
 #align language.supr_add Language.iSup_add
 
-/- warning: language.add_supr -> Language.add_iSup is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) m (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i))) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) m (l i)))
-but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) m (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i))) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) m (l i)))
-Case conversion may be inaccurate. Consider using '#align language.add_supr Language.add_iSupₓ'. -/
 theorem add_iSup {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
     (m + ⨆ i, l i) = ⨆ i, m + l i :=
   sup_iSup
 #align language.add_supr Language.add_iSup
 
-/- warning: language.mem_pow -> Language.mem_pow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {l : Language.{u1} α} {x : List.{u1} α} {n : Nat}, Iff (Membership.Mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (Language.hasMem.{u1} α) x (HPow.hPow.{u1, 0, u1} (Language.{u1} α) Nat (Language.{u1} α) (instHPow.{u1, 0} (Language.{u1} α) Nat (Monoid.Pow.{u1} (Language.{u1} α) (MonoidWithZero.toMonoid.{u1} (Language.{u1} α) (Semiring.toMonoidWithZero.{u1} (Language.{u1} α) (Language.semiring.{u1} α))))) l n)) (Exists.{succ u1} (List.{u1} (List.{u1} α)) (fun (S : List.{u1} (List.{u1} α)) => And (Eq.{succ u1} (List.{u1} α) x (List.join.{u1} α S)) (And (Eq.{1} Nat (List.length.{u1} (List.{u1} α) S) n) (forall (y : List.{u1} α), (Membership.Mem.{u1, u1} (List.{u1} α) (List.{u1} (List.{u1} α)) (List.hasMem.{u1} (List.{u1} α)) y S) -> (Membership.Mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (Language.hasMem.{u1} α) y l)))))
-but is expected to have type
-  forall {α : Type.{u1}} {l : Language.{u1} α} {x : List.{u1} α} {n : Nat}, Iff (Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x (HPow.hPow.{u1, 0, u1} (Language.{u1} α) Nat (Language.{u1} α) (instHPow.{u1, 0} (Language.{u1} α) Nat (Monoid.Pow.{u1} (Language.{u1} α) (MonoidWithZero.toMonoid.{u1} (Language.{u1} α) (Semiring.toMonoidWithZero.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))))) l n)) (Exists.{succ u1} (List.{u1} (List.{u1} α)) (fun (S : List.{u1} (List.{u1} α)) => And (Eq.{succ u1} (List.{u1} α) x (List.join.{u1} α S)) (And (Eq.{1} Nat (List.length.{u1} (List.{u1} α) S) n) (forall (y : List.{u1} α), (Membership.mem.{u1, u1} (List.{u1} α) (List.{u1} (List.{u1} α)) (List.instMembershipList.{u1} (List.{u1} α)) y S) -> (Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) y l)))))
-Case conversion may be inaccurate. Consider using '#align language.mem_pow Language.mem_powₓ'. -/
 theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
     x ∈ l ^ n ↔ ∃ S : List (List α), x = S.join ∧ S.length = n ∧ ∀ y ∈ S, y ∈ l :=
   by
@@ -359,12 +278,6 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
       exact ⟨a, _, hS.1, ⟨S, rfl, rfl, hS.2⟩, rfl⟩
 #align language.mem_pow Language.mem_pow
 
-/- warning: language.kstar_eq_supr_pow -> Language.kstar_eq_iSup_pow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l) (iSup.{u1, 1} (Language.{u1} α) (Set.hasSup.{u1} (List.{u1} α)) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} (Language.{u1} α) Nat (Language.{u1} α) (instHPow.{u1, 0} (Language.{u1} α) Nat (Monoid.Pow.{u1} (Language.{u1} α) (MonoidWithZero.toMonoid.{u1} (Language.{u1} α) (Semiring.toMonoidWithZero.{u1} (Language.{u1} α) (Language.semiring.{u1} α))))) l i))
-but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (KStar.kstar.{u1} (Language.{u1} α) (Language.instKStarLanguage.{u1} α) l) (iSup.{u1, 1} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} (Language.{u1} α) Nat (Language.{u1} α) (instHPow.{u1, 0} (Language.{u1} α) Nat (Monoid.Pow.{u1} (Language.{u1} α) (MonoidWithZero.toMonoid.{u1} (Language.{u1} α) (Semiring.toMonoidWithZero.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))))) l i))
-Case conversion may be inaccurate. Consider using '#align language.kstar_eq_supr_pow Language.kstar_eq_iSup_powₓ'. -/
 theorem kstar_eq_iSup_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
   by
   ext x
@@ -374,12 +287,6 @@ theorem kstar_eq_iSup_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
   · rintro ⟨_, S, rfl, rfl, hS⟩; exact ⟨S, rfl, hS⟩
 #align language.kstar_eq_supr_pow Language.kstar_eq_iSup_pow
 
-/- warning: language.map_kstar -> Language.map_kstar is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (l : Language.{u1} α), Eq.{succ u2} (Language.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l)) (KStar.kstar.{u2} (Language.{u2} β) (Language.hasKstar.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) l))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (l : Language.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u2} α) => Language.{u1} β) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (KStar.kstar.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u2} α) => Language.{u1} β) l) (Language.instKStarLanguage.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) l))
-Case conversion may be inaccurate. Consider using '#align language.map_kstar Language.map_kstarₓ'. -/
 @[simp]
 theorem map_kstar (f : α → β) (l : Language α) : map f l∗ = (map f l)∗ :=
   by
@@ -394,12 +301,6 @@ theorem mul_self_kstar_comm (l : Language α) : l∗ * l = l * l∗ := by
 #align language.mul_self_kstar_comm Language.mul_self_kstar_comm
 -/
 
-/- warning: language.one_add_self_mul_kstar_eq_kstar -> Language.one_add_self_mul_kstar_eq_kstar is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.hasAdd.{u1} α)) (OfNat.ofNat.{u1} (Language.{u1} α) 1 (OfNat.mk.{u1} (Language.{u1} α) 1 (One.one.{u1} (Language.{u1} α) (Language.hasOne.{u1} α)))) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.hasMul.{u1} α)) l (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l))) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l)
-but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) (OfNat.ofNat.{u1} (Language.{u1} α) 1 (One.toOfNat1.{u1} (Language.{u1} α) (Language.instOneLanguage.{u1} α))) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) l (KStar.kstar.{u1} (Language.{u1} α) (Language.instKStarLanguage.{u1} α) l))) (KStar.kstar.{u1} (Language.{u1} α) (Language.instKStarLanguage.{u1} α) l)
-Case conversion may be inaccurate. Consider using '#align language.one_add_self_mul_kstar_eq_kstar Language.one_add_self_mul_kstar_eq_kstarₓ'. -/
 @[simp]
 theorem one_add_self_mul_kstar_eq_kstar (l : Language α) : 1 + l * l∗ = l∗ :=
   by
@@ -407,12 +308,6 @@ theorem one_add_self_mul_kstar_eq_kstar (l : Language α) : 1 + l * l∗ = l∗
   exact sup_iSup_nat_succ _
 #align language.one_add_self_mul_kstar_eq_kstar Language.one_add_self_mul_kstar_eq_kstar
 
-/- warning: language.one_add_kstar_mul_self_eq_kstar -> Language.one_add_kstar_mul_self_eq_kstar is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.hasAdd.{u1} α)) (OfNat.ofNat.{u1} (Language.{u1} α) 1 (OfNat.mk.{u1} (Language.{u1} α) 1 (One.one.{u1} (Language.{u1} α) (Language.hasOne.{u1} α)))) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.hasMul.{u1} α)) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l) l)) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l)
-but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) (OfNat.ofNat.{u1} (Language.{u1} α) 1 (One.toOfNat1.{u1} (Language.{u1} α) (Language.instOneLanguage.{u1} α))) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) (KStar.kstar.{u1} (Language.{u1} α) (Language.instKStarLanguage.{u1} α) l) l)) (KStar.kstar.{u1} (Language.{u1} α) (Language.instKStarLanguage.{u1} α) l)
-Case conversion may be inaccurate. Consider using '#align language.one_add_kstar_mul_self_eq_kstar Language.one_add_kstar_mul_self_eq_kstarₓ'. -/
 @[simp]
 theorem one_add_kstar_mul_self_eq_kstar (l : Language α) : 1 + l∗ * l = l∗ := by
   rw [mul_self_kstar_comm, one_add_self_mul_kstar_eq_kstar]

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

@@ -348,10 +348,8 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
   induction' n with n ihn generalizing x
   · simp only [mem_one, pow_zero, length_eq_zero]
     constructor
-    · rintro rfl
-      exact ⟨[], rfl, rfl, fun y h => h.elim⟩
-    · rintro ⟨_, rfl, rfl, _⟩
-      rfl
+    · rintro rfl; exact ⟨[], rfl, rfl, fun y h => h.elim⟩
+    · rintro ⟨_, rfl, rfl, _⟩; rfl
   · simp only [pow_succ, mem_mul, ihn]
     constructor
     · rintro ⟨a, b, ha, ⟨S, rfl, rfl, hS⟩, rfl⟩
@@ -372,10 +370,8 @@ theorem kstar_eq_iSup_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
   ext x
   simp only [mem_kstar, mem_supr, mem_pow]
   constructor
-  · rintro ⟨S, rfl, hS⟩
-    exact ⟨_, S, rfl, rfl, hS⟩
-  · rintro ⟨_, S, rfl, rfl, hS⟩
-    exact ⟨S, rfl, hS⟩
+  · rintro ⟨S, rfl, hS⟩; exact ⟨_, S, rfl, rfl, hS⟩
+  · rintro ⟨_, S, rfl, rfl, hS⟩; exact ⟨S, rfl, hS⟩
 #align language.kstar_eq_supr_pow Language.kstar_eq_iSup_pow
 
 /- warning: language.map_kstar -> Language.map_kstar is a dubious translation:

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

@@ -231,10 +231,7 @@ theorem map_id (l : Language α) : map id l = l := by simp [map]
 #align language.map_id Language.map_id
 
 /- warning: language.map_map -> Language.map_map is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} (g : β -> γ) (f : α -> β) (l : Language.{u1} α), Eq.{succ u3} (Language.{u3} γ) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (fun (_x : RingHom.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) => (Language.{u2} β) -> (Language.{u3} γ)) (RingHom.hasCoeToFun.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (Language.map.{u2, u3} β γ g) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) l)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (fun (_x : RingHom.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) => (Language.{u1} α) -> (Language.{u3} γ)) (RingHom.hasCoeToFun.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (Language.map.{u1, u3} α γ (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) l)
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} (g : β -> γ) (f : α -> β) (l : Language.{u3} α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u1} β) => Language.{u2} γ) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (a : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u3} α) => Language.{u1} β) a) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (fun (_x : Language.{u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u1} β) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u1, u2} β γ g) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u3} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u3} α) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u3, u2} α γ (Function.comp.{succ u3, succ u1, succ u2} α β γ g f)) l)
+<too large>
 Case conversion may be inaccurate. Consider using '#align language.map_map Language.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β → γ) (f : α → β) (l : Language α) : map g (map f l) = map (g ∘ f) l := by

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

@@ -224,7 +224,7 @@ def map (f : α → β) : Language α →+* Language β
 lean 3 declaration is
   forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) (fun (_x : RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) => (Language.{u1} α) -> (Language.{u1} α)) (RingHom.hasCoeToFun.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
 but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u1} α) => Language.{u1} α) l) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (fun (_x : Language.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u1} α) => Language.{u1} α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (RingHom.instRingHomClassRingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
+  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u1} α) => Language.{u1} α) l) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (fun (_x : Language.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u1} α) => Language.{u1} α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (RingHom.instRingHomClassRingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
 Case conversion may be inaccurate. Consider using '#align language.map_id Language.map_idₓ'. -/
 @[simp]
 theorem map_id (l : Language α) : map id l = l := by simp [map]
@@ -234,7 +234,7 @@ theorem map_id (l : Language α) : map id l = l := by simp [map]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} (g : β -> γ) (f : α -> β) (l : Language.{u1} α), Eq.{succ u3} (Language.{u3} γ) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (fun (_x : RingHom.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) => (Language.{u2} β) -> (Language.{u3} γ)) (RingHom.hasCoeToFun.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (Language.map.{u2, u3} β γ g) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) l)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (fun (_x : RingHom.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) => (Language.{u1} α) -> (Language.{u3} γ)) (RingHom.hasCoeToFun.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (Language.map.{u1, u3} α γ (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) l)
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} (g : β -> γ) (f : α -> β) (l : Language.{u3} α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u1} β) => Language.{u2} γ) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (a : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u3} α) => Language.{u1} β) a) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (fun (_x : Language.{u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u1} β) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u1, u2} β γ g) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u3} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u3} α) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u3, u2} α γ (Function.comp.{succ u3, succ u1, succ u2} α β γ g f)) l)
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} (g : β -> γ) (f : α -> β) (l : Language.{u3} α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u1} β) => Language.{u2} γ) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (a : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u3} α) => Language.{u1} β) a) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (fun (_x : Language.{u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u1} β) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u1, u2} β γ g) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u3} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u3} α) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u3, u2} α γ (Function.comp.{succ u3, succ u1, succ u2} α β γ g f)) l)
 Case conversion may be inaccurate. Consider using '#align language.map_map Language.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β → γ) (f : α → β) (l : Language α) : map g (map f l) = map (g ∘ f) l := by
@@ -385,7 +385,7 @@ theorem kstar_eq_iSup_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (l : Language.{u1} α), Eq.{succ u2} (Language.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l)) (KStar.kstar.{u2} (Language.{u2} β) (Language.hasKstar.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) l))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (l : Language.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u2} α) => Language.{u1} β) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (KStar.kstar.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u2} α) => Language.{u1} β) l) (Language.instKStarLanguage.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) l))
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (l : Language.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u2} α) => Language.{u1} β) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (KStar.kstar.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u2} α) => Language.{u1} β) l) (Language.instKStarLanguage.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) l))
 Case conversion may be inaccurate. Consider using '#align language.map_kstar Language.map_kstarₓ'. -/
 @[simp]
 theorem map_kstar (f : α → β) (l : Language α) : map f l∗ = (map f l)∗ :=

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

@@ -285,59 +285,59 @@ theorem le_add_congr {l₁ l₂ m₁ m₂ : Language α} : l₁ ≤ m₁ → l
   sup_le_sup
 #align language.le_add_congr Language.le_add_congr
 
-/- warning: language.mem_supr -> Language.mem_supᵢ is a dubious translation:
+/- warning: language.mem_supr -> Language.mem_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} {l : ι -> (Language.{u2} α)} {x : List.{u2} α}, Iff (Membership.Mem.{u2, u2} (List.{u2} α) (Language.{u2} α) (Language.hasMem.{u2} α) x (supᵢ.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i))) (Exists.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} (List.{u2} α) (Language.{u2} α) (Language.hasMem.{u2} α) x (l i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} {l : ι -> (Language.{u2} α)} {x : List.{u2} α}, Iff (Membership.Mem.{u2, u2} (List.{u2} α) (Language.{u2} α) (Language.hasMem.{u2} α) x (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i))) (Exists.{u1} ι (fun (i : ι) => Membership.Mem.{u2, u2} (List.{u2} α) (Language.{u2} α) (Language.hasMem.{u2} α) x (l i)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} {l : ι -> (Language.{u1} α)} {x : List.{u1} α}, Iff (Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x (supᵢ.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i))) (Exists.{u2} ι (fun (i : ι) => Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x (l i)))
-Case conversion may be inaccurate. Consider using '#align language.mem_supr Language.mem_supᵢₓ'. -/
-theorem mem_supᵢ {ι : Sort v} {l : ι → Language α} {x : List α} : (x ∈ ⨆ i, l i) ↔ ∃ i, x ∈ l i :=
-  mem_unionᵢ
-#align language.mem_supr Language.mem_supᵢ
+  forall {α : Type.{u1}} {ι : Sort.{u2}} {l : ι -> (Language.{u1} α)} {x : List.{u1} α}, Iff (Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i))) (Exists.{u2} ι (fun (i : ι) => Membership.mem.{u1, u1} (List.{u1} α) (Language.{u1} α) (instMembershipListLanguage.{u1} α) x (l i)))
+Case conversion may be inaccurate. Consider using '#align language.mem_supr Language.mem_iSupₓ'. -/
+theorem mem_iSup {ι : Sort v} {l : ι → Language α} {x : List α} : (x ∈ ⨆ i, l i) ↔ ∃ i, x ∈ l i :=
+  mem_iUnion
+#align language.mem_supr Language.mem_iSup
 
-/- warning: language.supr_mul -> Language.supᵢ_mul is a dubious translation:
+/- warning: language.supr_mul -> Language.iSup_mul is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) (supᵢ.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i)) m) (supᵢ.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) (l i) m))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i)) m) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) (l i) m))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) (supᵢ.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i)) m) (supᵢ.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) (l i) m))
-Case conversion may be inaccurate. Consider using '#align language.supr_mul Language.supᵢ_mulₓ'. -/
-theorem supᵢ_mul {ι : Sort v} (l : ι → Language α) (m : Language α) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i)) m) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) (l i) m))
+Case conversion may be inaccurate. Consider using '#align language.supr_mul Language.iSup_mulₓ'. -/
+theorem iSup_mul {ι : Sort v} (l : ι → Language α) (m : Language α) :
     (⨆ i, l i) * m = ⨆ i, l i * m :=
-  image2_unionᵢ_left _ _ _
-#align language.supr_mul Language.supᵢ_mul
+  image2_iUnion_left _ _ _
+#align language.supr_mul Language.iSup_mul
 
-/- warning: language.mul_supr -> Language.mul_supᵢ is a dubious translation:
+/- warning: language.mul_supr -> Language.mul_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) m (supᵢ.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i))) (supᵢ.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) m (l i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) m (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i))) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HMul.hMul.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHMul.{u2} (Language.{u2} α) (Language.hasMul.{u2} α)) m (l i)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) m (supᵢ.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i))) (supᵢ.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) m (l i)))
-Case conversion may be inaccurate. Consider using '#align language.mul_supr Language.mul_supᵢₓ'. -/
-theorem mul_supᵢ {ι : Sort v} (l : ι → Language α) (m : Language α) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) m (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i))) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HMul.hMul.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHMul.{u1} (Language.{u1} α) (Language.instMulLanguage.{u1} α)) m (l i)))
+Case conversion may be inaccurate. Consider using '#align language.mul_supr Language.mul_iSupₓ'. -/
+theorem mul_iSup {ι : Sort v} (l : ι → Language α) (m : Language α) :
     (m * ⨆ i, l i) = ⨆ i, m * l i :=
-  image2_unionᵢ_right _ _ _
-#align language.mul_supr Language.mul_supᵢ
+  image2_iUnion_right _ _ _
+#align language.mul_supr Language.mul_iSup
 
-/- warning: language.supr_add -> Language.supᵢ_add is a dubious translation:
+/- warning: language.supr_add -> Language.iSup_add is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) (supᵢ.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i)) m) (supᵢ.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) (l i) m))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i)) m) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) (l i) m))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) (supᵢ.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i)) m) (supᵢ.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) (l i) m))
-Case conversion may be inaccurate. Consider using '#align language.supr_add Language.supᵢ_addₓ'. -/
-theorem supᵢ_add {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i)) m) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) (l i) m))
+Case conversion may be inaccurate. Consider using '#align language.supr_add Language.iSup_addₓ'. -/
+theorem iSup_add {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
     (⨆ i, l i) + m = ⨆ i, l i + m :=
-  supᵢ_sup
-#align language.supr_add Language.supᵢ_add
+  iSup_sup
+#align language.supr_add Language.iSup_add
 
-/- warning: language.add_supr -> Language.add_supᵢ is a dubious translation:
+/- warning: language.add_supr -> Language.add_iSup is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) m (supᵢ.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i))) (supᵢ.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) m (l i)))
+  forall {α : Type.{u2}} {ι : Sort.{u1}} [_inst_1 : Nonempty.{u1} ι] (l : ι -> (Language.{u2} α)) (m : Language.{u2} α), Eq.{succ u2} (Language.{u2} α) (HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) m (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => l i))) (iSup.{u2, u1} (Language.{u2} α) (Set.hasSup.{u2} (List.{u2} α)) ι (fun (i : ι) => HAdd.hAdd.{u2, u2, u2} (Language.{u2} α) (Language.{u2} α) (Language.{u2} α) (instHAdd.{u2} (Language.{u2} α) (Language.hasAdd.{u2} α)) m (l i)))
 but is expected to have type
-  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) m (supᵢ.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i))) (supᵢ.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) m (l i)))
-Case conversion may be inaccurate. Consider using '#align language.add_supr Language.add_supᵢₓ'. -/
-theorem add_supᵢ {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
+  forall {α : Type.{u1}} {ι : Sort.{u2}} [_inst_1 : Nonempty.{u2} ι] (l : ι -> (Language.{u1} α)) (m : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) m (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => l i))) (iSup.{u1, u2} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) ι (fun (i : ι) => HAdd.hAdd.{u1, u1, u1} (Language.{u1} α) (Language.{u1} α) (Language.{u1} α) (instHAdd.{u1} (Language.{u1} α) (Language.instAddLanguage.{u1} α)) m (l i)))
+Case conversion may be inaccurate. Consider using '#align language.add_supr Language.add_iSupₓ'. -/
+theorem add_iSup {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
     (m + ⨆ i, l i) = ⨆ i, m + l i :=
-  sup_supᵢ
-#align language.add_supr Language.add_supᵢ
+  sup_iSup
+#align language.add_supr Language.add_iSup
 
 /- warning: language.mem_pow -> Language.mem_pow is a dubious translation:
 lean 3 declaration is
@@ -364,13 +364,13 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
       exact ⟨a, _, hS.1, ⟨S, rfl, rfl, hS.2⟩, rfl⟩
 #align language.mem_pow Language.mem_pow
 
-/- warning: language.kstar_eq_supr_pow -> Language.kstar_eq_supᵢ_pow is a dubious translation:
+/- warning: language.kstar_eq_supr_pow -> Language.kstar_eq_iSup_pow is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l) (supᵢ.{u1, 1} (Language.{u1} α) (Set.hasSup.{u1} (List.{u1} α)) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} (Language.{u1} α) Nat (Language.{u1} α) (instHPow.{u1, 0} (Language.{u1} α) Nat (Monoid.Pow.{u1} (Language.{u1} α) (MonoidWithZero.toMonoid.{u1} (Language.{u1} α) (Semiring.toMonoidWithZero.{u1} (Language.{u1} α) (Language.semiring.{u1} α))))) l i))
+  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l) (iSup.{u1, 1} (Language.{u1} α) (Set.hasSup.{u1} (List.{u1} α)) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} (Language.{u1} α) Nat (Language.{u1} α) (instHPow.{u1, 0} (Language.{u1} α) Nat (Monoid.Pow.{u1} (Language.{u1} α) (MonoidWithZero.toMonoid.{u1} (Language.{u1} α) (Semiring.toMonoidWithZero.{u1} (Language.{u1} α) (Language.semiring.{u1} α))))) l i))
 but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (KStar.kstar.{u1} (Language.{u1} α) (Language.instKStarLanguage.{u1} α) l) (supᵢ.{u1, 1} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} (Language.{u1} α) Nat (Language.{u1} α) (instHPow.{u1, 0} (Language.{u1} α) Nat (Monoid.Pow.{u1} (Language.{u1} α) (MonoidWithZero.toMonoid.{u1} (Language.{u1} α) (Semiring.toMonoidWithZero.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))))) l i))
-Case conversion may be inaccurate. Consider using '#align language.kstar_eq_supr_pow Language.kstar_eq_supᵢ_powₓ'. -/
-theorem kstar_eq_supᵢ_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
+  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (KStar.kstar.{u1} (Language.{u1} α) (Language.instKStarLanguage.{u1} α) l) (iSup.{u1, 1} (Language.{u1} α) (CompleteBooleanAlgebra.toSupSet.{u1} (Language.{u1} α) (instCompleteBooleanAlgebraLanguage.{u1} α)) Nat (fun (i : Nat) => HPow.hPow.{u1, 0, u1} (Language.{u1} α) Nat (Language.{u1} α) (instHPow.{u1, 0} (Language.{u1} α) Nat (Monoid.Pow.{u1} (Language.{u1} α) (MonoidWithZero.toMonoid.{u1} (Language.{u1} α) (Semiring.toMonoidWithZero.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))))) l i))
+Case conversion may be inaccurate. Consider using '#align language.kstar_eq_supr_pow Language.kstar_eq_iSup_powₓ'. -/
+theorem kstar_eq_iSup_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
   by
   ext x
   simp only [mem_kstar, mem_supr, mem_pow]
@@ -379,7 +379,7 @@ theorem kstar_eq_supᵢ_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
     exact ⟨_, S, rfl, rfl, hS⟩
   · rintro ⟨_, S, rfl, rfl, hS⟩
     exact ⟨S, rfl, hS⟩
-#align language.kstar_eq_supr_pow Language.kstar_eq_supᵢ_pow
+#align language.kstar_eq_supr_pow Language.kstar_eq_iSup_pow
 
 /- warning: language.map_kstar -> Language.map_kstar is a dubious translation:
 lean 3 declaration is
@@ -411,7 +411,7 @@ Case conversion may be inaccurate. Consider using '#align language.one_add_self_
 theorem one_add_self_mul_kstar_eq_kstar (l : Language α) : 1 + l * l∗ = l∗ :=
   by
   simp only [kstar_eq_supr_pow, mul_supr, ← pow_succ, ← pow_zero l]
-  exact sup_supᵢ_nat_succ _
+  exact sup_iSup_nat_succ _
 #align language.one_add_self_mul_kstar_eq_kstar Language.one_add_self_mul_kstar_eq_kstar
 
 /- warning: language.one_add_kstar_mul_self_eq_kstar -> Language.one_add_kstar_mul_self_eq_kstar is a dubious translation:
@@ -434,7 +434,7 @@ instance : KleeneAlgebra (Language α) :=
     kstar_mul_le_self := fun l m h =>
       by
       rw [kstar_eq_supr_pow, supr_mul]
-      refine' supᵢ_le fun n => _
+      refine' iSup_le fun n => _
       induction' n with n ih
       · simp
       rw [pow_succ', mul_assoc (l ^ n) l m]
@@ -442,7 +442,7 @@ instance : KleeneAlgebra (Language α) :=
     mul_kstar_le_self := fun l m h =>
       by
       rw [kstar_eq_supr_pow, mul_supr]
-      refine' supᵢ_le fun n => _
+      refine' iSup_le fun n => _
       induction' n with n ih
       · simp
       rw [pow_succ, ← mul_assoc m l (l ^ n)]

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

@@ -224,7 +224,7 @@ def map (f : α → β) : Language α →+* Language β
 lean 3 declaration is
   forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) (fun (_x : RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) => (Language.{u1} α) -> (Language.{u1} α)) (RingHom.hasCoeToFun.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
 but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u1} α) => Language.{u1} α) l) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (fun (_x : Language.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u1} α) => Language.{u1} α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (RingHom.instRingHomClassRingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
+  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u1} α) => Language.{u1} α) l) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (fun (_x : Language.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u1} α) => Language.{u1} α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (RingHom.instRingHomClassRingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
 Case conversion may be inaccurate. Consider using '#align language.map_id Language.map_idₓ'. -/
 @[simp]
 theorem map_id (l : Language α) : map id l = l := by simp [map]
@@ -234,7 +234,7 @@ theorem map_id (l : Language α) : map id l = l := by simp [map]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} (g : β -> γ) (f : α -> β) (l : Language.{u1} α), Eq.{succ u3} (Language.{u3} γ) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (fun (_x : RingHom.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) => (Language.{u2} β) -> (Language.{u3} γ)) (RingHom.hasCoeToFun.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (Language.map.{u2, u3} β γ g) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) l)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (fun (_x : RingHom.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) => (Language.{u1} α) -> (Language.{u3} γ)) (RingHom.hasCoeToFun.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (Language.map.{u1, u3} α γ (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) l)
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} (g : β -> γ) (f : α -> β) (l : Language.{u3} α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u1} β) => Language.{u2} γ) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (a : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u3} α) => Language.{u1} β) a) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (fun (_x : Language.{u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u1} β) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u1, u2} β γ g) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u3} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u3} α) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u3, u2} α γ (Function.comp.{succ u3, succ u1, succ u2} α β γ g f)) l)
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} (g : β -> γ) (f : α -> β) (l : Language.{u3} α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u1} β) => Language.{u2} γ) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (a : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u3} α) => Language.{u1} β) a) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (fun (_x : Language.{u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u1} β) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u1, u2} β γ g) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u3} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u3} α) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u3, u2} α γ (Function.comp.{succ u3, succ u1, succ u2} α β γ g f)) l)
 Case conversion may be inaccurate. Consider using '#align language.map_map Language.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β → γ) (f : α → β) (l : Language α) : map g (map f l) = map (g ∘ f) l := by
@@ -385,7 +385,7 @@ theorem kstar_eq_supᵢ_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (l : Language.{u1} α), Eq.{succ u2} (Language.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l)) (KStar.kstar.{u2} (Language.{u2} β) (Language.hasKstar.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) l))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (l : Language.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u2} α) => Language.{u1} β) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (KStar.kstar.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u2} α) => Language.{u1} β) l) (Language.instKStarLanguage.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) l))
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (l : Language.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u2} α) => Language.{u1} β) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (KStar.kstar.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u2} α) => Language.{u1} β) l) (Language.instKStarLanguage.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) l))
 Case conversion may be inaccurate. Consider using '#align language.map_kstar Language.map_kstarₓ'. -/
 @[simp]
 theorem map_kstar (f : α → β) (l : Language α) : map f l∗ = (map f l)∗ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -224,7 +224,7 @@ def map (f : α → β) : Language α →+* Language β
 lean 3 declaration is
   forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} (Language.{u1} α) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) (fun (_x : RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) => (Language.{u1} α) -> (Language.{u1} α)) (RingHom.hasCoeToFun.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
 but is expected to have type
-  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u1} α) => Language.{u1} α) l) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (fun (_x : Language.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u1} α) => Language.{u1} α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (RingHom.instRingHomClassRingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
+  forall {α : Type.{u1}} (l : Language.{u1} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u1} α) => Language.{u1} α) l) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (fun (_x : Language.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u1} α) => Language.{u1} α) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α))) (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (RingHom.instRingHomClassRingHom.{u1, u1} (Language.{u1} α) (Language.{u1} α) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.instSemiringLanguage.{u1} α)))))) (Language.map.{u1, u1} α α (id.{succ u1} α)) l) l
 Case conversion may be inaccurate. Consider using '#align language.map_id Language.map_idₓ'. -/
 @[simp]
 theorem map_id (l : Language α) : map id l = l := by simp [map]
@@ -234,7 +234,7 @@ theorem map_id (l : Language α) : map id l = l := by simp [map]
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} (g : β -> γ) (f : α -> β) (l : Language.{u1} α), Eq.{succ u3} (Language.{u3} γ) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (fun (_x : RingHom.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) => (Language.{u2} β) -> (Language.{u3} γ)) (RingHom.hasCoeToFun.{u2, u3} (Language.{u2} β) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (Language.map.{u2, u3} β γ g) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) l)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (fun (_x : RingHom.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) => (Language.{u1} α) -> (Language.{u3} γ)) (RingHom.hasCoeToFun.{u1, u3} (Language.{u1} α) (Language.{u3} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} γ) (Language.semiring.{u3} γ))) (Language.map.{u1, u3} α γ (Function.comp.{succ u1, succ u2, succ u3} α β γ g f)) l)
 but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} (g : β -> γ) (f : α -> β) (l : Language.{u3} α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u1} β) => Language.{u2} γ) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (a : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u3} α) => Language.{u1} β) a) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (fun (_x : Language.{u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u1} β) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u1, u2} β γ g) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u3} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u3} α) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u3, u2} α γ (Function.comp.{succ u3, succ u1, succ u2} α β γ g f)) l)
+  forall {α : Type.{u3}} {β : Type.{u1}} {γ : Type.{u2}} (g : β -> γ) (f : α -> β) (l : Language.{u3} α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u1} β) => Language.{u2} γ) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (a : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u3} α) => Language.{u1} β) a) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (fun (_x : Language.{u1} β) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u1} β) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u1, u2} (Language.{u1} β) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u1, u2} β γ g) (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u3} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, u3, u1} (RingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u3, u1} (Language.{u3} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u3, u1} α β f) l)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (fun (_x : Language.{u3} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u3} α) => Language.{u2} γ) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonUnitalNonAssocSemiring.toMul.{u3} (Language.{u3} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)))) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Language.{u3} α) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u2, u3, u2} (RingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ))) (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)) (RingHom.instRingHomClassRingHom.{u3, u2} (Language.{u3} α) (Language.{u2} γ) (Semiring.toNonAssocSemiring.{u3} (Language.{u3} α) (Language.instSemiringLanguage.{u3} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} γ) (Language.instSemiringLanguage.{u2} γ)))))) (Language.map.{u3, u2} α γ (Function.comp.{succ u3, succ u1, succ u2} α β γ g f)) l)
 Case conversion may be inaccurate. Consider using '#align language.map_map Language.map_mapₓ'. -/
 @[simp]
 theorem map_map (g : β → γ) (f : α → β) (l : Language α) : map g (map f l) = map (g ∘ f) l := by
@@ -385,7 +385,7 @@ theorem kstar_eq_supᵢ_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i :=
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (l : Language.{u1} α), Eq.{succ u2} (Language.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) (KStar.kstar.{u1} (Language.{u1} α) (Language.hasKstar.{u1} α) l)) (KStar.kstar.{u2} (Language.{u2} β) (Language.hasKstar.{u2} β) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (fun (_x : RingHom.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) => (Language.{u1} α) -> (Language.{u2} β)) (RingHom.hasCoeToFun.{u1, u2} (Language.{u1} α) (Language.{u2} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} α) (Language.semiring.{u1} α)) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} β) (Language.semiring.{u2} β))) (Language.map.{u1, u2} α β f) l))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (l : Language.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u2} α) => Language.{u1} β) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (KStar.kstar.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u2} α) => Language.{u1} β) l) (Language.instKStarLanguage.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) l))
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (l : Language.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u2} α) => Language.{u1} β) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) (KStar.kstar.{u2} (Language.{u2} α) (Language.instKStarLanguage.{u2} α) l)) (KStar.kstar.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u2} α) => Language.{u1} β) l) (Language.instKStarLanguage.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (fun (_x : Language.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Language.{u2} α) => Language.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonUnitalNonAssocSemiring.toMul.{u2} (Language.{u2} α) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Language.{u2} α) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Language.{u1} β) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β))) (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)) (RingHom.instRingHomClassRingHom.{u2, u1} (Language.{u2} α) (Language.{u1} β) (Semiring.toNonAssocSemiring.{u2} (Language.{u2} α) (Language.instSemiringLanguage.{u2} α)) (Semiring.toNonAssocSemiring.{u1} (Language.{u1} β) (Language.instSemiringLanguage.{u1} β)))))) (Language.map.{u2, u1} α β f) l))
 Case conversion may be inaccurate. Consider using '#align language.map_kstar Language.map_kstarₓ'. -/
 @[simp]
 theorem map_kstar (f : α → β) (l : Language α) : map f l∗ = (map f l)∗ :=

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

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -240,7 +240,7 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
       exact ⟨[], rfl, rfl, fun _ h ↦ by contradiction⟩
     · rintro ⟨_, rfl, rfl, _⟩
       rfl
-  · simp only [pow_succ, mem_mul, ihn]
+  · simp only [pow_succ', mem_mul, ihn]
     constructor
     · rintro ⟨a, ha, b, ⟨S, rfl, rfl, hS⟩, rfl⟩
       exact ⟨a :: S, rfl, rfl, forall_mem_cons.2 ⟨ha, hS⟩⟩
@@ -272,7 +272,7 @@ theorem mul_self_kstar_comm (l : Language α) : l∗ * l = l * l∗ := by
 
 @[simp]
 theorem one_add_self_mul_kstar_eq_kstar (l : Language α) : 1 + l * l∗ = l∗ := by
-  simp only [kstar_eq_iSup_pow, mul_iSup, ← pow_succ, ← pow_zero l]
+  simp only [kstar_eq_iSup_pow, mul_iSup, ← pow_succ', ← pow_zero l]
   exact sup_iSup_nat_succ _
 #align language.one_add_self_mul_kstar_eq_kstar Language.one_add_self_mul_kstar_eq_kstar
 
@@ -292,15 +292,15 @@ instance : KleeneAlgebra (Language α) :=
       refine' iSup_le (fun n ↦ _)
       induction' n with n ih
       · simp
-      rw [pow_succ', mul_assoc (l^n) l m]
+      rw [pow_succ, mul_assoc (l^n) l m]
       exact le_trans (le_mul_congr le_rfl h) ih,
     mul_kstar_le_self := fun l m h ↦ by
       rw [kstar_eq_iSup_pow, mul_iSup]
       refine' iSup_le (fun n ↦ _)
       induction' n with n ih
       · simp
-      rw [pow_succ, ← mul_assoc m l (l^n)]
-      exact le_trans (le_mul_congr h le_rfl) ih }
+      rw [pow_succ, ← mul_assoc m (l^n) l]
+      exact le_trans (le_mul_congr ih le_rfl) h }
 
 /-- Language `l.reverse` is defined as the set of words from `l` backwards. -/
 def reverse (l : Language α) : Language α := { w : List α | w.reverse ∈ l }

This PR removes the default values for nsmul and zsmul, forcing the user to populate them manually. The previous behavior can be obtained by writing nsmul := nsmulRec and zsmul := zsmulRec, which is now in the docstring for these fields.

The motivation here is to make it more obvious when module diamonds are being introduced, or at least where they might be hiding; you can now simply search for nsmulRec in the source code.

Arguably we should do the same thing for intCast, natCast, pow, and zpow too, but diamonds are less common in those fields, so I'll leave them to a subsequent PR.

Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -151,6 +151,7 @@ instance instSemiring : Semiring (Language α) where
   natCast_succ n := by cases n <;> simp [Nat.cast, add_def, zero_def]
   left_distrib _ _ _ := image2_union_right
   right_distrib _ _ _ := image2_union_left
+  nsmul := nsmulRec
 
 @[simp]
 theorem add_self (l : Language α) : l + l = l :=

Those lemmas have historically been very annoying to use in rw since all their arguments were implicit. One too many people complained about it on Zulip, so I'm changing them.

Downstream code broken by this change can fix it by adding appropriately many _s.

Also marks CauSeq.ext @[ext].

Order.BoundedOrder

• top_sup_eq
• sup_top_eq
• bot_sup_eq
• sup_bot_eq
• top_inf_eq
• inf_top_eq
• bot_inf_eq
• inf_bot_eq

Order.Lattice

• sup_idem
• sup_comm
• sup_assoc
• sup_left_idem
• sup_right_idem
• inf_idem
• inf_comm
• inf_assoc
• inf_left_idem
• inf_right_idem
• sup_inf_left
• sup_inf_right
• inf_sup_left
• inf_sup_right

Order.MinMax

• max_min_distrib_left
• max_min_distrib_right
• min_max_distrib_left
• min_max_distrib_right

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -154,7 +154,7 @@ instance instSemiring : Semiring (Language α) where
 
 @[simp]
 theorem add_self (l : Language α) : l + l = l :=
-  sup_idem
+  sup_idem _
 #align language.add_self Language.add_self
 
 /-- Maps the alphabet of a language. -/

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

@@ -179,11 +179,10 @@ lemma mem_kstar_iff_exists_nonempty {x : List α} :
     x ∈ l∗ ↔ ∃ S : List (List α), x = S.join ∧ ∀ y ∈ S, y ∈ l ∧ y ≠ [] := by
   constructor
   · rintro ⟨S, rfl, h⟩
-    refine' ⟨S.filter fun l ↦ ¬List.isEmpty l, by simp, fun y hy ↦ _⟩
+    refine' ⟨S.filter fun l ↦ !List.isEmpty l, by simp, fun y hy ↦ _⟩
     -- Porting note: The previous code was:
     -- rw [mem_filter, empty_iff_eq_nil] at hy
-    rw [mem_filter, decide_not, Bool.decide_coe, Bool.not_eq_true', ← Bool.bool_iff_false,
-      isEmpty_iff_eq_nil] at hy
+    rw [mem_filter, Bool.not_eq_true', ← Bool.bool_iff_false, isEmpty_iff_eq_nil] at hy
     exact ⟨h y hy.1, hy.2⟩
   · rintro ⟨S, hx, h⟩
     exact ⟨S, hx, fun y hy ↦ (h y hy).1⟩

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -1,7 +1,7 @@
 /-
 Copyright (c) 2020 Fox Thomson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Fox Thomson
+Authors: Fox Thomson, Martin Dvorak
 -/
 import Mathlib.Algebra.Order.Kleene
 import Mathlib.Algebra.Ring.Hom.Defs
@@ -14,10 +14,12 @@ import Mathlib.Tactic.DeriveFintype
 /-!
 # Languages
 
-This file contains the definition and operations on formal languages over an alphabet. Note strings
-are implemented as lists over the alphabet.
-The operations in this file define a [Kleene algebra](https://en.wikipedia.org/wiki/Kleene_algebra)
+This file contains the definition and operations on formal languages over an alphabet.
+Note that "strings" are implemented as lists over the alphabet.
+Union and concatenation define a [Kleene algebra](https://en.wikipedia.org/wiki/Kleene_algebra)
 over the languages.
+In addition to that, we define a reversal of a language and prove that it behaves well
+with respect to other language operations.
 -/
 
 
@@ -300,6 +302,76 @@ instance : KleeneAlgebra (Language α) :=
       rw [pow_succ, ← mul_assoc m l (l^n)]
       exact le_trans (le_mul_congr h le_rfl) ih }
 
+/-- Language `l.reverse` is defined as the set of words from `l` backwards. -/
+def reverse (l : Language α) : Language α := { w : List α | w.reverse ∈ l }
+
+@[simp]
+lemma mem_reverse : a ∈ l.reverse ↔ a.reverse ∈ l := Iff.rfl
+
+lemma reverse_mem_reverse : a.reverse ∈ l.reverse ↔ a ∈ l := by
+  rw [mem_reverse, List.reverse_reverse]
+
+lemma reverse_eq_image (l : Language α) : l.reverse = List.reverse '' l :=
+  ((List.reverse_involutive.toPerm _).image_eq_preimage _).symm
+
+@[simp]
+lemma reverse_zero : (0 : Language α).reverse = 0 := rfl
+
+@[simp]
+lemma reverse_one : (1 : Language α).reverse = 1 := by
+  simp [reverse, ← one_def]
+
+lemma reverse_involutive : Function.Involutive (reverse : Language α → _) :=
+  List.reverse_involutive.preimage
+
+lemma reverse_bijective : Function.Bijective (reverse : Language α → _) :=
+  reverse_involutive.bijective
+
+lemma reverse_injective : Function.Injective (reverse : Language α → _) :=
+  reverse_involutive.injective
+
+lemma reverse_surjective : Function.Surjective (reverse : Language α → _) :=
+  reverse_involutive.surjective
+
+@[simp]
+lemma reverse_reverse (l : Language α) : l.reverse.reverse = l := reverse_involutive l
+
+@[simp]
+lemma reverse_add (l m : Language α) : (l + m).reverse = l.reverse + m.reverse := rfl
+
+@[simp]
+lemma reverse_mul (l m : Language α) : (l * m).reverse = m.reverse * l.reverse := by
+  simp only [mul_def, reverse_eq_image, image2_image_left, image2_image_right, image_image2,
+    List.reverse_append]
+  apply image2_swap
+
+@[simp]
+lemma reverse_iSup {ι : Sort*} (l : ι → Language α) : (⨆ i, l i).reverse = ⨆ i, (l i).reverse :=
+  preimage_iUnion
+
+@[simp]
+lemma reverse_iInf {ι : Sort*} (l : ι → Language α) : (⨅ i, l i).reverse = ⨅ i, (l i).reverse :=
+  preimage_iInter
+
+variable (α) in
+/-- `Language.reverse` as a ring isomorphism to the opposite ring. -/
+@[simps]
+def reverseIso : Language α ≃+* (Language α)ᵐᵒᵖ where
+  toFun l := .op l.reverse
+  invFun l' := l'.unop.reverse
+  left_inv := reverse_reverse
+  right_inv l' := MulOpposite.unop_injective <| reverse_reverse l'.unop
+  map_mul' l₁ l₂ := MulOpposite.unop_injective <| reverse_mul l₁ l₂
+  map_add' l₁ l₂ := MulOpposite.unop_injective <| reverse_add l₁ l₂
+
+@[simp]
+lemma reverse_pow (l : Language α) (n : ℕ) : (l ^ n).reverse = l.reverse ^ n :=
+  MulOpposite.op_injective (map_pow (reverseIso α) l n)
+
+@[simp]
+lemma reverse_kstar (l : Language α) : l∗.reverse = l.reverse∗ := by
+  simp only [kstar_eq_iSup_pow, reverse_iSup, reverse_pow]
+
 end Language
 
 /-- Symbols for use by all kinds of grammars. -/

• Redefine Set.image2 to use ∃ a ∈ s, ∃ b ∈ t, f a b = c instead of ∃ a b, a ∈ s ∧ b ∈ t ∧ f a b = c.
• Redefine Set.seq as Set.image2. The new definition is equal to the old one but rw [Set.seq] gives a different result.
• Redefine Filter.map₂ to use ∃ u ∈ f, ∃ v ∈ g, image2 m u v ⊆ s instead of ∃ u v, u ∈ f ∧ v ∈ g ∧ ...
• Update lemmas like Set.mem_image2, Finset.mem_image₂, Set.mem_mul, Finset.mem_div etc

The two reasons to make the change are:

• ∃ a ∈ s, ∃ b ∈ t, _ is a simp-normal form, and
• it looks a bit nicer.

@@ -110,7 +110,7 @@ theorem mem_add (l m : Language α) (x : List α) : x ∈ l + m ↔ x ∈ l ∨
   Iff.rfl
 #align language.mem_add Language.mem_add
 
-theorem mem_mul : x ∈ l * m ↔ ∃ a b, a ∈ l ∧ b ∈ m ∧ a ++ b = x :=
+theorem mem_mul : x ∈ l * m ↔ ∃ a ∈ l, ∃ b ∈ m, a ++ b = x :=
   mem_image2
 #align language.mem_mul Language.mem_mul
 
@@ -240,11 +240,11 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
       rfl
   · simp only [pow_succ, mem_mul, ihn]
     constructor
-    · rintro ⟨a, b, ha, ⟨S, rfl, rfl, hS⟩, rfl⟩
+    · rintro ⟨a, ha, b, ⟨S, rfl, rfl, hS⟩, rfl⟩
       exact ⟨a :: S, rfl, rfl, forall_mem_cons.2 ⟨ha, hS⟩⟩
     · rintro ⟨_ | ⟨a, S⟩, rfl, hn, hS⟩ <;> cases hn
       rw [forall_mem_cons] at hS
-      exact ⟨a, _, hS.1, ⟨S, rfl, rfl, hS.2⟩, rfl⟩
+      exact ⟨a, hS.1, _, ⟨S, rfl, rfl, hS.2⟩, rfl⟩
 #align language.mem_pow Language.mem_pow
 
 theorem kstar_eq_iSup_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i := by

Golf a proof. Also add Language.mem_kstar_iff_exists_nonempty.

@@ -173,9 +173,8 @@ theorem map_map (g : β → γ) (f : α → β) (l : Language α) : map g (map f
   simp [map, image_image]
 #align language.map_map Language.map_map
 
-theorem kstar_def_nonempty (l : Language α) :
-    l∗ = { x | ∃ S : List (List α), x = S.join ∧ ∀ y ∈ S, y ∈ l ∧ y ≠ [] } := by
-  ext x
+lemma mem_kstar_iff_exists_nonempty {x : List α} :
+    x ∈ l∗ ↔ ∃ S : List (List α), x = S.join ∧ ∀ y ∈ S, y ∈ l ∧ y ≠ [] := by
   constructor
   · rintro ⟨S, rfl, h⟩
     refine' ⟨S.filter fun l ↦ ¬List.isEmpty l, by simp, fun y hy ↦ _⟩
@@ -186,6 +185,10 @@ theorem kstar_def_nonempty (l : Language α) :
     exact ⟨h y hy.1, hy.2⟩
   · rintro ⟨S, hx, h⟩
     exact ⟨S, hx, fun y hy ↦ (h y hy).1⟩
+
+theorem kstar_def_nonempty (l : Language α) :
+    l∗ = { x | ∃ S : List (List α), x = S.join ∧ ∀ y ∈ S, y ∈ l ∧ y ≠ [] } := by
+  ext x; apply mem_kstar_iff_exists_nonempty
 #align language.kstar_def_nonempty Language.kstar_def_nonempty
 
 theorem le_iff (l m : Language α) : l ≤ m ↔ l + m = m :=

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

@@ -294,7 +294,7 @@ instance : KleeneAlgebra (Language α) :=
       refine' iSup_le (fun n ↦ _)
       induction' n with n ih
       · simp
-      rw [pow_succ, ←mul_assoc m l (l^n)]
+      rw [pow_succ, ← mul_assoc m l (l^n)]
       exact le_trans (le_mul_congr h le_rfl) ih }
 
 end Language

I believe the file defining a type of morphisms belongs alongside the file defining the structure this morphism works on. So I would like to reorganize the files in the Mathlib.Algebra.Hom folder so that e.g. Mathlib.Algebra.Hom.Ring becomes Mathlib.Algebra.Ring.Hom and Mathlib.Algebra.Hom.NonUnitalAlg becomes Mathlib.Algebra.Algebra.NonUnitalHom.

While fixing the imports I went ahead and sorted them for good luck.

The full list of changes is: renamed: Mathlib/Algebra/Hom/NonUnitalAlg.lean -> Mathlib/Algebra/Algebra/NonUnitalHom.lean renamed: Mathlib/Algebra/Hom/Aut.lean -> Mathlib/Algebra/Group/Aut.lean renamed: Mathlib/Algebra/Hom/Commute.lean -> Mathlib/Algebra/Group/Commute/Hom.lean renamed: Mathlib/Algebra/Hom/Embedding.lean -> Mathlib/Algebra/Group/Embedding.lean renamed: Mathlib/Algebra/Hom/Equiv/Basic.lean -> Mathlib/Algebra/Group/Equiv/Basic.lean renamed: Mathlib/Algebra/Hom/Equiv/TypeTags.lean -> Mathlib/Algebra/Group/Equiv/TypeTags.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/Basic.lean -> Mathlib/Algebra/Group/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/GroupWithZero.lean -> Mathlib/Algebra/GroupWithZero/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Freiman.lean -> Mathlib/Algebra/Group/Freiman.lean renamed: Mathlib/Algebra/Hom/Group/Basic.lean -> Mathlib/Algebra/Group/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Group/Defs.lean -> Mathlib/Algebra/Group/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/GroupAction.lean -> Mathlib/GroupTheory/GroupAction/Hom.lean renamed: Mathlib/Algebra/Hom/GroupInstances.lean -> Mathlib/Algebra/Group/Hom/Instances.lean renamed: Mathlib/Algebra/Hom/Iterate.lean -> Mathlib/Algebra/GroupPower/IterateHom.lean renamed: Mathlib/Algebra/Hom/Centroid.lean -> Mathlib/Algebra/Ring/CentroidHom.lean renamed: Mathlib/Algebra/Hom/Ring/Basic.lean -> Mathlib/Algebra/Ring/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Ring/Defs.lean -> Mathlib/Algebra/Ring/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/Units.lean -> Mathlib/Algebra/Group/Units/Hom.lean

Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Reorganizing.20.60Mathlib.2EAlgebra.2EHom.60

@@ -3,8 +3,8 @@ Copyright (c) 2020 Fox Thomson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Fox Thomson
 -/
-import Mathlib.Algebra.Hom.Ring.Defs
 import Mathlib.Algebra.Order.Kleene
+import Mathlib.Algebra.Ring.Hom.Defs
 import Mathlib.Data.List.Join
 import Mathlib.Data.Set.Lattice
 import Mathlib.Tactic.DeriveFintype

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Alex J Best <alex.j.best@gmail.com>

@@ -7,6 +7,7 @@ import Mathlib.Algebra.Hom.Ring.Defs
 import Mathlib.Algebra.Order.Kleene
 import Mathlib.Data.List.Join
 import Mathlib.Data.Set.Lattice
+import Mathlib.Tactic.DeriveFintype
 
 #align_import computability.language from "leanprover-community/mathlib"@"a239cd3e7ac2c7cde36c913808f9d40c411344f6"
 
@@ -297,3 +298,14 @@ instance : KleeneAlgebra (Language α) :=
       exact le_trans (le_mul_congr h le_rfl) ih }
 
 end Language
+
+/-- Symbols for use by all kinds of grammars. -/
+inductive Symbol (T N : Type*)
+  /-- Terminal symbols (of the same type as the language) -/
+  | terminal    (t : T) : Symbol T N
+  /-- Nonterminal symbols (must not be present at the end of word being generated) -/
+  | nonterminal (n : N) : Symbol T N
+deriving
+  DecidableEq, Repr, Fintype
+
+attribute [nolint docBlame] Symbol.proxyType Symbol.proxyTypeEquiv

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Fox Thomson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Fox Thomson
 -/
-import Mathlib.Algebra.Hom.Ring
+import Mathlib.Algebra.Hom.Ring.Defs
 import Mathlib.Algebra.Order.Kleene
 import Mathlib.Data.List.Join
 import Mathlib.Data.Set.Lattice

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

This has nice performance benefits.

@@ -24,7 +24,7 @@ open List Set Computability
 
 universe v
 
-variable {α β γ : Type _}
+variable {α β γ : Type*}
 
 /-- A language is a set of strings over an alphabet. -/
 def Language (α) :=

@@ -129,7 +129,7 @@ theorem nil_mem_kstar (l : Language α) : [] ∈ l∗ :=
   ⟨[], rfl, fun _ h ↦ by contradiction⟩
 #align language.nil_mem_kstar Language.nil_mem_kstar
 
-instance : Semiring (Language α) where
+instance instSemiring : Semiring (Language α) where
   add := (· + ·)
   add_assoc := union_assoc
   zero := 0
@@ -178,16 +178,11 @@ theorem kstar_def_nonempty (l : Language α) :
   constructor
   · rintro ⟨S, rfl, h⟩
     refine' ⟨S.filter fun l ↦ ¬List.isEmpty l, by simp, fun y hy ↦ _⟩
-    simp [mem_filter, List.isEmpty_iff_eq_nil] at hy
     -- Porting note: The previous code was:
-    -- exact ⟨h y hy.1, hy.2⟩
-    --
-    -- The goal `y ≠ []` for the second argument cannot be resolved
-    -- by `hy.2 : isEmpty y = False`.
-    let ⟨hyl, hyr⟩ := hy
-    apply And.intro (h y hyl)
-    cases y <;> simp only [ne_eq, not_true, not_false_iff]
-    contradiction
+    -- rw [mem_filter, empty_iff_eq_nil] at hy
+    rw [mem_filter, decide_not, Bool.decide_coe, Bool.not_eq_true', ← Bool.bool_iff_false,
+      isEmpty_iff_eq_nil] at hy
+    exact ⟨h y hy.1, hy.2⟩
   · rintro ⟨S, hx, h⟩
     exact ⟨S, hx, fun y hy ↦ (h y hy).1⟩
 #align language.kstar_def_nonempty Language.kstar_def_nonempty
@@ -237,15 +232,8 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
     constructor
     · rintro rfl
       exact ⟨[], rfl, rfl, fun _ h ↦ by contradiction⟩
-    · -- Porting note: The previous code was:
-      -- rintro ⟨_, rfl, rfl, _⟩
-      -- rfl
-      --
-      -- The code reports an error for the second `rfl`.
-      rintro ⟨_, rfl, h₀, _⟩
-      simp; intros _ h₁
-      rw [h₀] at h₁
-      contradiction
+    · rintro ⟨_, rfl, rfl, _⟩
+      rfl
   · simp only [pow_succ, mem_mul, ihn]
     constructor
     · rintro ⟨a, b, ha, ⟨S, rfl, rfl, hS⟩, rfl⟩
@@ -288,7 +276,7 @@ theorem one_add_kstar_mul_self_eq_kstar (l : Language α) : 1 + l∗ * l = l∗
 #align language.one_add_kstar_mul_self_eq_kstar Language.one_add_kstar_mul_self_eq_kstar
 
 instance : KleeneAlgebra (Language α) :=
-  { Language.instSemiringLanguage, Set.completeAtomicBooleanAlgebra with
+  { Language.instSemiring, Set.completeAtomicBooleanAlgebra with
     kstar := fun L ↦ L∗,
     one_le_kstar := fun a l hl ↦ ⟨[], hl, by simp⟩,
     mul_kstar_le_kstar := fun a ↦ (one_add_self_mul_kstar_eq_kstar a).le.trans' le_sup_right,

• Use {x | p x} instead of fun x ↦ p x to define a set here and there.
• Golf some proofs.
• Replace Con.ker_apply_eq_preimage with Con.ker_apply. The old version used to abuse definitional equality between Set M and M → Prop.
• Fix Submonoid.mk* lemmas to use ⟨_, _⟩, not ⟨⟨_, _⟩, _⟩.

@@ -45,14 +45,13 @@ variable {l m : Language α} {a b x : List α}
 
 /-- Zero language has no elements. -/
 instance : Zero (Language α) :=
-  ⟨fun _ => False⟩
+  ⟨(∅ : Set _)⟩
 
 /-- `1 : Language α` contains only one element `[]`. -/
 instance : One (Language α) :=
-  ⟨fun l => l = []⟩
+  ⟨{[]}⟩
 
-instance : Inhabited (Language α) :=
-  ⟨fun _ => False⟩
+instance : Inhabited (Language α) := ⟨(∅ : Set _)⟩
 
 /-- The sum of two languages is their union. -/
 instance : Add (Language α) :=

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Fox Thomson. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Fox Thomson
-
-! This file was ported from Lean 3 source module computability.language
-! leanprover-community/mathlib commit a239cd3e7ac2c7cde36c913808f9d40c411344f6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Hom.Ring
 import Mathlib.Algebra.Order.Kleene
 import Mathlib.Data.List.Join
 import Mathlib.Data.Set.Lattice
 
+#align_import computability.language from "leanprover-community/mathlib"@"a239cd3e7ac2c7cde36c913808f9d40c411344f6"
+
 /-!
 # Languages
 

Adds new CompletelyDistribLattice/CompleteAtomicBooleanAlgebra classes for complete lattices / complete atomic Boolean algebras that are also completely distributive, and removes the misleading claim that CompleteDistribLattice/CompleteBooleanAlgebra are completely distributive.

• Product/pi/order dual instances for completely distributive lattices, etc.
• Every complete linear order is a completely distributive lattice.
• Every atomic complete Boolean algebra is a complete atomic Boolean algebra.
• Every complete atomic Boolean algebra is indeed (co)atom(ist)ic.
• Atom(ist)ic orders are closed under pis.
• All existing types with CompleteDistribLattice instances are upgraded to CompletelyDistribLattice.
• All existing types with CompleteBooleanAlgebra instances are upgraded to CompleteAtomicBooleanAlgebra.

See related discussion on Zulip.

@@ -37,7 +37,7 @@ def Language (α) :=
 instance : Membership (List α) (Language α) := ⟨Set.Mem⟩
 instance : Singleton (List α) (Language α) := ⟨Set.singleton⟩
 instance : Insert (List α) (Language α) := ⟨Set.insert⟩
-instance : CompleteBooleanAlgebra (Language α) := Set.instCompleteBooleanAlgebraSet
+instance : CompleteAtomicBooleanAlgebra (Language α) := Set.completeAtomicBooleanAlgebra
 
 namespace Language
 
@@ -292,7 +292,7 @@ theorem one_add_kstar_mul_self_eq_kstar (l : Language α) : 1 + l∗ * l = l∗
 #align language.one_add_kstar_mul_self_eq_kstar Language.one_add_kstar_mul_self_eq_kstar
 
 instance : KleeneAlgebra (Language α) :=
-  { Language.instSemiringLanguage, Set.instCompleteBooleanAlgebraSet with
+  { Language.instSemiringLanguage, Set.completeAtomicBooleanAlgebra with
     kstar := fun L ↦ L∗,
     one_le_kstar := fun a l hl ↦ ⟨[], hl, by simp⟩,
     mul_kstar_le_kstar := fun a ↦ (one_add_self_mul_kstar_eq_kstar a).le.trans' le_sup_right,

• depends on: https://github.com/leanprover/std4/pull/163
• depends on: #5584
• depends on: #5715
• depends on: #5729
• depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -248,7 +248,6 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
       -- The code reports an error for the second `rfl`.
       rintro ⟨_, rfl, h₀, _⟩
       simp; intros _ h₁
-      rw [length_eq_zero] at h₀
       rw [h₀] at h₁
       contradiction
   · simp only [pow_succ, mem_mul, ihn]

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -202,7 +202,7 @@ theorem le_iff (l m : Language α) : l ≤ m ↔ l + m = m :=
 
 theorem le_mul_congr {l₁ l₂ m₁ m₂ : Language α} : l₁ ≤ m₁ → l₂ ≤ m₂ → l₁ * l₂ ≤ m₁ * m₂ := by
   intro h₁ h₂ x hx
-  simp only [mul_def, exists_and_left, mem_image2, image_prod] at hx⊢
+  simp only [mul_def, exists_and_left, mem_image2, image_prod] at hx ⊢
   tauto
 #align language.le_mul_congr Language.le_mul_congr
 

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

@@ -187,7 +187,7 @@ theorem kstar_def_nonempty (l : Language α) :
     -- exact ⟨h y hy.1, hy.2⟩
     --
     -- The goal `y ≠ []` for the second argument cannot be resolved
-    -- by `hy.2 : isEmpty y = false`.
+    -- by `hy.2 : isEmpty y = False`.
     let ⟨hyl, hyr⟩ := hy
     apply And.intro (h y hyl)
     cases y <;> simp only [ne_eq, not_true, not_false_iff]

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>

@@ -210,29 +210,29 @@ theorem le_add_congr {l₁ l₂ m₁ m₂ : Language α} : l₁ ≤ m₁ → l
   sup_le_sup
 #align language.le_add_congr Language.le_add_congr
 
-theorem mem_supᵢ {ι : Sort v} {l : ι → Language α} {x : List α} : (x ∈ ⨆ i, l i) ↔ ∃ i, x ∈ l i :=
-  mem_unionᵢ
-#align language.mem_supr Language.mem_supᵢ
+theorem mem_iSup {ι : Sort v} {l : ι → Language α} {x : List α} : (x ∈ ⨆ i, l i) ↔ ∃ i, x ∈ l i :=
+  mem_iUnion
+#align language.mem_supr Language.mem_iSup
 
-theorem supᵢ_mul {ι : Sort v} (l : ι → Language α) (m : Language α) :
+theorem iSup_mul {ι : Sort v} (l : ι → Language α) (m : Language α) :
     (⨆ i, l i) * m = ⨆ i, l i * m :=
-  image2_unionᵢ_left _ _ _
-#align language.supr_mul Language.supᵢ_mul
+  image2_iUnion_left _ _ _
+#align language.supr_mul Language.iSup_mul
 
-theorem mul_supᵢ {ι : Sort v} (l : ι → Language α) (m : Language α) :
+theorem mul_iSup {ι : Sort v} (l : ι → Language α) (m : Language α) :
     (m * ⨆ i, l i) = ⨆ i, m * l i :=
-  image2_unionᵢ_right _ _ _
-#align language.mul_supr Language.mul_supᵢ
+  image2_iUnion_right _ _ _
+#align language.mul_supr Language.mul_iSup
 
-theorem supᵢ_add {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
+theorem iSup_add {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
     (⨆ i, l i) + m = ⨆ i, l i + m :=
-  supᵢ_sup
-#align language.supr_add Language.supᵢ_add
+  iSup_sup
+#align language.supr_add Language.iSup_add
 
-theorem add_supᵢ {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
+theorem add_iSup {ι : Sort v} [Nonempty ι] (l : ι → Language α) (m : Language α) :
     (m + ⨆ i, l i) = ⨆ i, m + l i :=
-  sup_supᵢ
-#align language.add_supr Language.add_supᵢ
+  sup_iSup
+#align language.add_supr Language.add_iSup
 
 theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
     x ∈ l ^ n ↔ ∃ S : List (List α), x = S.join ∧ S.length = n ∧ ∀ y ∈ S, y ∈ l := by
@@ -260,31 +260,31 @@ theorem mem_pow {l : Language α} {x : List α} {n : ℕ} :
       exact ⟨a, _, hS.1, ⟨S, rfl, rfl, hS.2⟩, rfl⟩
 #align language.mem_pow Language.mem_pow
 
-theorem kstar_eq_supᵢ_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i := by
+theorem kstar_eq_iSup_pow (l : Language α) : l∗ = ⨆ i : ℕ, l ^ i := by
   ext x
-  simp only [mem_kstar, mem_supᵢ, mem_pow]
+  simp only [mem_kstar, mem_iSup, mem_pow]
   constructor
   · rintro ⟨S, rfl, hS⟩
     exact ⟨_, S, rfl, rfl, hS⟩
   · rintro ⟨_, S, rfl, rfl, hS⟩
     exact ⟨S, rfl, hS⟩
-#align language.kstar_eq_supr_pow Language.kstar_eq_supᵢ_pow
+#align language.kstar_eq_supr_pow Language.kstar_eq_iSup_pow
 
 @[simp]
 theorem map_kstar (f : α → β) (l : Language α) : map f l∗ = (map f l)∗ := by
-  rw [kstar_eq_supᵢ_pow, kstar_eq_supᵢ_pow]
+  rw [kstar_eq_iSup_pow, kstar_eq_iSup_pow]
   simp_rw [← map_pow]
-  exact image_unionᵢ
+  exact image_iUnion
 #align language.map_kstar Language.map_kstar
 
 theorem mul_self_kstar_comm (l : Language α) : l∗ * l = l * l∗ := by
-  simp only [kstar_eq_supᵢ_pow, mul_supᵢ, supᵢ_mul, ← pow_succ, ← pow_succ']
+  simp only [kstar_eq_iSup_pow, mul_iSup, iSup_mul, ← pow_succ, ← pow_succ']
 #align language.mul_self_kstar_comm Language.mul_self_kstar_comm
 
 @[simp]
 theorem one_add_self_mul_kstar_eq_kstar (l : Language α) : 1 + l * l∗ = l∗ := by
-  simp only [kstar_eq_supᵢ_pow, mul_supᵢ, ← pow_succ, ← pow_zero l]
-  exact sup_supᵢ_nat_succ _
+  simp only [kstar_eq_iSup_pow, mul_iSup, ← pow_succ, ← pow_zero l]
+  exact sup_iSup_nat_succ _
 #align language.one_add_self_mul_kstar_eq_kstar Language.one_add_self_mul_kstar_eq_kstar
 
 @[simp]
@@ -299,15 +299,15 @@ instance : KleeneAlgebra (Language α) :=
     mul_kstar_le_kstar := fun a ↦ (one_add_self_mul_kstar_eq_kstar a).le.trans' le_sup_right,
     kstar_mul_le_kstar := fun a ↦ (one_add_kstar_mul_self_eq_kstar a).le.trans' le_sup_right,
     kstar_mul_le_self := fun l m h ↦ by
-      rw [kstar_eq_supᵢ_pow, supᵢ_mul]
-      refine' supᵢ_le (fun n ↦ _)
+      rw [kstar_eq_iSup_pow, iSup_mul]
+      refine' iSup_le (fun n ↦ _)
       induction' n with n ih
       · simp
       rw [pow_succ', mul_assoc (l^n) l m]
       exact le_trans (le_mul_congr le_rfl h) ih,
     mul_kstar_le_self := fun l m h ↦ by
-      rw [kstar_eq_supᵢ_pow, mul_supᵢ]
-      refine' supᵢ_le (fun n ↦ _)
+      rw [kstar_eq_iSup_pow, mul_iSup]
+      refine' iSup_le (fun n ↦ _)
       induction' n with n ih
       · simp
       rw [pow_succ, ←mul_assoc m l (l^n)]

This is another case of https://github.com/leanprover/lean4/issues/2096

@@ -292,10 +292,9 @@ theorem one_add_kstar_mul_self_eq_kstar (l : Language α) : 1 + l∗ * l = l∗
   rw [mul_self_kstar_comm, one_add_self_mul_kstar_eq_kstar]
 #align language.one_add_kstar_mul_self_eq_kstar Language.one_add_kstar_mul_self_eq_kstar
 
--- Porting note: `noncomputable` required.
-noncomputable instance : KleeneAlgebra (Language α) :=
-  { Language.instSemiringLanguage, Set.instCompleteBooleanAlgebraSet,
-      Language.instKStarLanguage with
+instance : KleeneAlgebra (Language α) :=
+  { Language.instSemiringLanguage, Set.instCompleteBooleanAlgebraSet with
+    kstar := fun L ↦ L∗,
     one_le_kstar := fun a l hl ↦ ⟨[], hl, by simp⟩,
     mul_kstar_le_kstar := fun a ↦ (one_add_self_mul_kstar_eq_kstar a).le.trans' le_sup_right,
     kstar_mul_le_kstar := fun a ↦ (one_add_kstar_mul_self_eq_kstar a).le.trans' le_sup_right,

@@ -44,7 +44,7 @@ namespace Language
 variable {l m : Language α} {a b x : List α}
 
 -- Porting note: `reducible` attribute cannot be local.
-attribute [reducible] Language
+-- attribute [local reducible] Language
 
 /-- Zero language has no elements. -/
 instance : Zero (Language α) :=
@@ -59,7 +59,7 @@ instance : Inhabited (Language α) :=
 
 /-- The sum of two languages is their union. -/
 instance : Add (Language α) :=
-  ⟨(· ∪ ·)⟩
+  ⟨((· ∪ ·) : Set (List α) → Set (List α) → Set (List α))⟩
 
 /-- The product of two languages `l` and `m` is the language made of the strings `x ++ y` where
 `x ∈ l` and `y ∈ m`. -/
@@ -70,11 +70,11 @@ theorem zero_def : (0 : Language α) = (∅ : Set _) :=
   rfl
 #align language.zero_def Language.zero_def
 
-theorem one_def : (1 : Language α) = {[]} :=
+theorem one_def : (1 : Language α) = ({[]} : Set (List α)) :=
   rfl
 #align language.one_def Language.one_def
 
-theorem add_def (l m : Language α) : l + m = l ∪ m :=
+theorem add_def (l m : Language α) : l + m = (l ∪ m : Set (List α)) :=
   rfl
 #align language.add_def Language.add_def
 
@@ -90,6 +90,12 @@ lemma kstar_def (l : Language α) : l∗ = {x | ∃ L : List (List α), x = L.jo
   rfl
 #align language.kstar_def Language.kstar_def
 
+-- Porting note: `reducible` attribute cannot be local,
+--               so this new theorem is required in place of `Set.ext`.
+@[ext]
+theorem ext {l m : Language α} (h : ∀ (x : List α), x ∈ l ↔ x ∈ m) : l = m :=
+  Set.ext h
+
 @[simp]
 theorem not_mem_zero (x : List α) : x ∉ (0 : Language α) :=
   id

Co-authored-by: qawbecrdtey <40463813+qawbecrdtey@users.noreply.github.com> Co-authored-by: Komyyy <pol_tta@outlook.jp>