algebra.free_monoid.basic | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

657df433

(last sync)

refactor(linear_algebra/tensor_product): make lift f (x ⊗ₜ y) = f x y true by rfl (#18121)

Since this is essentially the "primitive" recursor, it is very convenient for it to expand definitionally.

With this change, the following lemmas are now rfl:

algebra.mul'_apply
free_monoid.lift_comp_of
free_monoid.lift_eval_of
tensor_product.lie_module.lift_apply
alternating_map.dom_coprod'_apply
contract_left_apply
contract_right_apply
dual_tensor_hom_apply
derivation.tensor_product_to_tmul
poly_equiv_tensor.to_fun_linear_tmul_apply
tensor_product.lift.tmul
tensor_product.lift.tmul'
algebra.tensor_product.lift_tmul
algebra.tensor_product.lmul'_apply_tmul
tensor_product.algebra.smul_def

And one lemma is no longer rfl

free_monoid.lift_apply

Diff

@@ -136,27 +136,41 @@ lemma hom_eq ⦃f g : free_monoid α →* M⦄ (h : ∀ x, f (of x) = g (of x))
 monoid_hom.ext $ λ l, rec_on l (f.map_one.trans g.map_one.symm) $
   λ x xs hxs, by simp only [h, hxs, monoid_hom.map_mul]
 
+/-- A variant of `list.prod` that has `[x].prod = x` true definitionally.
+
+The purpose is to make `free_monoid.lift_eval_of` true by `rfl`. -/
+@[to_additive "A variant of `list.sum` that has `[x].sum = x` true definitionally.
+
+The purpose is to make `free_add_monoid.lift_eval_of` true by `rfl`."]
+def prod_aux {M} [monoid M] (l : list M) : M :=
+l.rec_on 1 (λ x xs (_ : M), list.foldl (*) x xs)
+
+@[to_additive]
+lemma prod_aux_eq : ∀ l : list M, free_monoid.prod_aux l = l.prod
+| [] := rfl
+| (x :: xs) := congr_arg (λ x, list.foldl (*) x xs) (one_mul _).symm
+
 /-- Equivalence between maps `α → M` and monoid homomorphisms `free_monoid α →* M`. -/
 @[to_additive "Equivalence between maps `α → A` and additive monoid homomorphisms
 `free_add_monoid α →+ A`."]
 def lift : (α → M) ≃ (free_monoid α →* M) :=
-{ to_fun := λ f, ⟨λ l, (l.to_list.map f).prod, rfl,
-    λ l₁ l₂, by simp only [to_list_mul, list.map_append, list.prod_append]⟩,
+{ to_fun := λ f, ⟨λ l, free_monoid.prod_aux (l.to_list.map f), rfl,
+    λ l₁ l₂, by simp only [prod_aux_eq, to_list_mul, list.map_append, list.prod_append]⟩,
   inv_fun := λ f x, f (of x),
-  left_inv := λ f, funext $ λ x, one_mul (f x),
-  right_inv := λ f, hom_eq $ λ x, one_mul (f (of x)) }
+  left_inv := λ f, rfl,
+  right_inv := λ f, hom_eq $ λ x, rfl }
 
 @[simp, to_additive]
 lemma lift_symm_apply (f : free_monoid α →* M) : lift.symm f = f ∘ of := rfl
 
 @[to_additive]
-lemma lift_apply (f : α → M) (l : free_monoid α) : lift f l = (l.to_list.map f).prod := rfl
+lemma lift_apply (f : α → M) (l : free_monoid α) : lift f l = (l.to_list.map f).prod :=
+prod_aux_eq _
 
-@[to_additive] lemma lift_comp_of (f : α → M) : lift f ∘ of = f := lift.symm_apply_apply f
+@[to_additive] lemma lift_comp_of (f : α → M) : lift f ∘ of = f := rfl
 
 @[simp, to_additive]
-lemma lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x :=
-congr_fun (lift_comp_of f) x
+lemma lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x := rfl
 
 @[simp, to_additive]
 lemma lift_restrict (f : free_monoid α →* M) : lift (f ∘ of) = f :=

dd71334d

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

657df433

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Simon Hudon. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon, Yury Kudryashov
 -/
-import Data.List.BigOperators.Basic
+import Algebra.BigOperators.List.Basic
 
 #align_import algebra.free_monoid.basic from "leanprover-community/mathlib"@"657df4339ae6ceada048c8a2980fb10e393143ec"

657df433

bump to nightly-2024-01-21-06

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

65cf895d

Diff

@@ -114,8 +114,8 @@ instance : CancelMonoid (FreeMonoid α)
   mul_one := List.append_nil
   one_mul := List.nil_append
   mul_assoc := List.append_assoc
-  hMul_left_cancel _ _ _ := List.append_left_cancel
-  hMul_right_cancel _ _ _ := List.append_right_cancel
+  hMul_left_cancel _ _ _ := List.append_cancel_left
+  hMul_right_cancel _ _ _ := List.append_cancel_right
 
 @[to_additive]
 instance : Inhabited (FreeMonoid α) :=

657df433

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Simon Hudon. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon, Yury Kudryashov
 -/
-import Mathbin.Data.List.BigOperators.Basic
+import Data.List.BigOperators.Basic
 
 #align_import algebra.free_monoid.basic from "leanprover-community/mathlib"@"657df4339ae6ceada048c8a2980fb10e393143ec"

657df433

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -114,8 +114,8 @@ instance : CancelMonoid (FreeMonoid α)
   mul_one := List.append_nil
   one_mul := List.nil_append
   mul_assoc := List.append_assoc
-  mul_left_cancel _ _ _ := List.append_left_cancel
-  mul_right_cancel _ _ _ := List.append_right_cancel
+  hMul_left_cancel _ _ _ := List.append_left_cancel
+  hMul_right_cancel _ _ _ := List.append_right_cancel
 
 @[to_additive]
 instance : Inhabited (FreeMonoid α) :=
@@ -389,7 +389,7 @@ def mkMulAction (f : α → β → β) : MulAction (FreeMonoid α) β
     where
   smul l b := l.toList.foldr f b
   one_smul x := rfl
-  mul_smul xs ys b := List.foldr_append _ _ _ _
+  hMul_smul xs ys b := List.foldr_append _ _ _ _
 #align free_monoid.mk_mul_action FreeMonoid.mkMulAction
 #align free_add_monoid.mk_add_action FreeAddMonoid.mkAddAction
 -/

657df433

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2019 Simon Hudon. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon, Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.free_monoid.basic
-! leanprover-community/mathlib commit 657df4339ae6ceada048c8a2980fb10e393143ec
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.List.BigOperators.Basic
 
+#align_import algebra.free_monoid.basic from "leanprover-community/mathlib"@"657df4339ae6ceada048c8a2980fb10e393143ec"
+
 /-!
 # Free monoid over a given alphabet

657df433

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -221,6 +221,7 @@ theorem of_injective : Function.Injective (@of α) :=
 #align free_add_monoid.of_injective FreeAddMonoid.of_injective
 -/
 
+#print FreeMonoid.recOn /-
 /-- Recursor for `free_monoid` using `1` and `free_monoid.of x * xs` instead of `[]` and
 `x :: xs`. -/
 @[elab_as_elim,
@@ -231,21 +232,27 @@ def recOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
   List.recOn xs h0 ih
 #align free_monoid.rec_on FreeMonoid.recOn
 #align free_add_monoid.rec_on FreeAddMonoid.recOn
+-/
 
+#print FreeMonoid.recOn_one /-
 @[simp, to_additive]
 theorem recOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C xs → C (of x * xs)) :
     @recOn α C 1 h0 ih = h0 :=
   rfl
 #align free_monoid.rec_on_one FreeMonoid.recOn_one
 #align free_add_monoid.rec_on_zero FreeAddMonoid.recOn_zero
+-/
 
+#print FreeMonoid.recOn_of_mul /-
 @[simp, to_additive]
 theorem recOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C xs → C (of x * xs)) : @recOn α C (of x * xs) h0 ih = ih x xs (recOn xs h0 ih) :=
   rfl
 #align free_monoid.rec_on_of_mul FreeMonoid.recOn_of_mul
 #align free_add_monoid.rec_on_of_add FreeAddMonoid.recOn_of_add
+-/
 
+#print FreeMonoid.casesOn /-
 /-- A version of `list.cases_on` for `free_monoid` using `1` and `free_monoid.of x * xs` instead of
 `[]` and `x :: xs`. -/
 @[elab_as_elim,
@@ -256,21 +263,27 @@ def casesOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
   List.casesOn xs h0 ih
 #align free_monoid.cases_on FreeMonoid.casesOn
 #align free_add_monoid.cases_on FreeAddMonoid.casesOn
+-/
 
+#print FreeMonoid.casesOn_one /-
 @[simp, to_additive]
 theorem casesOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C (of x * xs)) :
     @casesOn α C 1 h0 ih = h0 :=
   rfl
 #align free_monoid.cases_on_one FreeMonoid.casesOn_one
 #align free_add_monoid.cases_on_zero FreeAddMonoid.casesOn_zero
+-/
 
+#print FreeMonoid.casesOn_of_mul /-
 @[simp, to_additive]
 theorem casesOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C (of x * xs)) : @casesOn α C (of x * xs) h0 ih = ih x xs :=
   rfl
 #align free_monoid.cases_on_of_mul FreeMonoid.casesOn_of_mul
 #align free_add_monoid.cases_on_of_add FreeAddMonoid.casesOn_of_add
+-/
 
+#print FreeMonoid.hom_eq /-
 @[ext, to_additive]
 theorem hom_eq ⦃f g : FreeMonoid α →* M⦄ (h : ∀ x, f (of x) = g (of x)) : f = g :=
   MonoidHom.ext fun l =>
@@ -278,6 +291,7 @@ theorem hom_eq ⦃f g : FreeMonoid α →* M⦄ (h : ∀ x, f (of x) = g (of x))
       simp only [h, hxs, MonoidHom.map_mul]
 #align free_monoid.hom_eq FreeMonoid.hom_eq
 #align free_add_monoid.hom_eq FreeAddMonoid.hom_eq
+-/
 
 #print FreeMonoid.prodAux /-
 /-- A variant of `list.prod` that has `[x].prod = x` true definitionally.
@@ -291,13 +305,16 @@ def prodAux {M} [Monoid M] (l : List M) : M :=
 #align free_add_monoid.sum_aux FreeAddMonoid.sumAux
 -/
 
+#print FreeMonoid.prodAux_eq /-
 @[to_additive]
 theorem prodAux_eq : ∀ l : List M, FreeMonoid.prodAux l = l.Prod
   | [] => rfl
   | x :: xs => congr_arg (fun x => List.foldl (· * ·) x xs) (one_mul _).symm
 #align free_monoid.prod_aux_eq FreeMonoid.prodAux_eq
 #align free_add_monoid.sum_aux_eq FreeAddMonoid.sumAux_eq
+-/
 
+#print FreeMonoid.lift /-
 /-- Equivalence between maps `α → M` and monoid homomorphisms `free_monoid α →* M`. -/
 @[to_additive
       "Equivalence between maps `α → A` and additive monoid homomorphisms\n`free_add_monoid α →+ A`."]
@@ -311,48 +328,64 @@ def lift : (α → M) ≃ (FreeMonoid α →* M)
   right_inv f := hom_eq fun x => rfl
 #align free_monoid.lift FreeMonoid.lift
 #align free_add_monoid.lift FreeAddMonoid.lift
+-/
 
+#print FreeMonoid.lift_symm_apply /-
 @[simp, to_additive]
 theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of :=
   rfl
 #align free_monoid.lift_symm_apply FreeMonoid.lift_symm_apply
 #align free_add_monoid.lift_symm_apply FreeAddMonoid.lift_symm_apply
+-/
 
+#print FreeMonoid.lift_apply /-
 @[to_additive]
 theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = (l.toList.map f).Prod :=
   prodAux_eq _
 #align free_monoid.lift_apply FreeMonoid.lift_apply
 #align free_add_monoid.lift_apply FreeAddMonoid.lift_apply
+-/
 
+#print FreeMonoid.lift_comp_of /-
 @[to_additive]
 theorem lift_comp_of (f : α → M) : lift f ∘ of = f :=
   rfl
 #align free_monoid.lift_comp_of FreeMonoid.lift_comp_of
 #align free_add_monoid.lift_comp_of FreeAddMonoid.lift_comp_of
+-/
 
+#print FreeMonoid.lift_eval_of /-
 @[simp, to_additive]
 theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x :=
   rfl
 #align free_monoid.lift_eval_of FreeMonoid.lift_eval_of
 #align free_add_monoid.lift_eval_of FreeAddMonoid.lift_eval_of
+-/
 
+#print FreeMonoid.lift_restrict /-
 @[simp, to_additive]
 theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f :=
   lift.apply_symm_apply f
 #align free_monoid.lift_restrict FreeMonoid.lift_restrict
 #align free_add_monoid.lift_restrict FreeAddMonoid.lift_restrict
+-/
 
+#print FreeMonoid.comp_lift /-
 @[to_additive]
 theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) := by ext; simp
 #align free_monoid.comp_lift FreeMonoid.comp_lift
 #align free_add_monoid.comp_lift FreeAddMonoid.comp_lift
+-/
 
+#print FreeMonoid.hom_map_lift /-
 @[to_additive]
 theorem hom_map_lift (g : M →* N) (f : α → M) (x : FreeMonoid α) : g (lift f x) = lift (g ∘ f) x :=
   MonoidHom.ext_iff.1 (comp_lift g f) x
 #align free_monoid.hom_map_lift FreeMonoid.hom_map_lift
 #align free_add_monoid.hom_map_lift FreeAddMonoid.hom_map_lift
+-/
 
+#print FreeMonoid.mkMulAction /-
 /-- Define a multiplicative action of `free_monoid α` on `β`. -/
 @[to_additive "Define an additive action of `free_add_monoid α` on `β`."]
 def mkMulAction (f : α → β → β) : MulAction (FreeMonoid α) β
@@ -362,7 +395,9 @@ def mkMulAction (f : α → β → β) : MulAction (FreeMonoid α) β
   mul_smul xs ys b := List.foldr_append _ _ _ _
 #align free_monoid.mk_mul_action FreeMonoid.mkMulAction
 #align free_add_monoid.mk_add_action FreeAddMonoid.mkAddAction
+-/
 
+#print FreeMonoid.smul_def /-
 @[to_additive]
 theorem smul_def (f : α → β → β) (l : FreeMonoid α) (b : β) :
     haveI := mk_mul_action f
@@ -370,7 +405,9 @@ theorem smul_def (f : α → β → β) (l : FreeMonoid α) (b : β) :
   rfl
 #align free_monoid.smul_def FreeMonoid.smul_def
 #align free_add_monoid.vadd_def FreeAddMonoid.vadd_def
+-/
 
+#print FreeMonoid.ofList_smul /-
 @[to_additive]
 theorem ofList_smul (f : α → β → β) (l : List α) (b : β) :
     haveI := mk_mul_action f
@@ -378,6 +415,7 @@ theorem ofList_smul (f : α → β → β) (l : List α) (b : β) :
   rfl
 #align free_monoid.of_list_smul FreeMonoid.ofList_smul
 #align free_add_monoid.of_list_vadd FreeAddMonoid.ofList_vadd
+-/
 
 #print FreeMonoid.of_smul /-
 @[simp, to_additive]
@@ -390,6 +428,7 @@ theorem of_smul (f : α → β → β) (x : α) (y : β) :
 #align free_add_monoid.of_vadd FreeAddMonoid.of_vadd
 -/
 
+#print FreeMonoid.map /-
 /-- The unique monoid homomorphism `free_monoid α →* free_monoid β` that sends
 each `of x` to `of (f x)`. -/
 @[to_additive
@@ -401,42 +440,55 @@ def map (f : α → β) : FreeMonoid α →* FreeMonoid β
   map_mul' l₁ l₂ := List.map_append _ _ _
 #align free_monoid.map FreeMonoid.map
 #align free_add_monoid.map FreeAddMonoid.map
+-/
 
+#print FreeMonoid.map_of /-
 @[simp, to_additive]
 theorem map_of (f : α → β) (x : α) : map f (of x) = of (f x) :=
   rfl
 #align free_monoid.map_of FreeMonoid.map_of
 #align free_add_monoid.map_of FreeAddMonoid.map_of
+-/
 
+#print FreeMonoid.toList_map /-
 @[to_additive]
 theorem toList_map (f : α → β) (xs : FreeMonoid α) : (map f xs).toList = xs.toList.map f :=
   rfl
 #align free_monoid.to_list_map FreeMonoid.toList_map
 #align free_add_monoid.to_list_map FreeAddMonoid.toList_map
+-/
 
+#print FreeMonoid.ofList_map /-
 @[to_additive]
 theorem ofList_map (f : α → β) (xs : List α) : ofList (xs.map f) = map f (ofList xs) :=
   rfl
 #align free_monoid.of_list_map FreeMonoid.ofList_map
 #align free_add_monoid.of_list_map FreeAddMonoid.ofList_map
+-/
 
+#print FreeMonoid.lift_of_comp_eq_map /-
 @[to_additive]
 theorem lift_of_comp_eq_map (f : α → β) : (lift fun x => of (f x)) = map f :=
   hom_eq fun x => rfl
 #align free_monoid.lift_of_comp_eq_map FreeMonoid.lift_of_comp_eq_map
 #align free_add_monoid.lift_of_comp_eq_map FreeAddMonoid.lift_of_comp_eq_map
+-/
 
+#print FreeMonoid.map_comp /-
 @[to_additive]
 theorem map_comp (g : β → γ) (f : α → β) : map (g ∘ f) = (map g).comp (map f) :=
   hom_eq fun x => rfl
 #align free_monoid.map_comp FreeMonoid.map_comp
 #align free_add_monoid.map_comp FreeAddMonoid.map_comp
+-/
 
+#print FreeMonoid.map_id /-
 @[simp, to_additive]
 theorem map_id : map (@id α) = MonoidHom.id (FreeMonoid α) :=
   hom_eq fun x => rfl
 #align free_monoid.map_id FreeMonoid.map_id
 #align free_add_monoid.map_id FreeAddMonoid.map_id
+-/
 
 end FreeMonoid

657df433

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -221,12 +221,6 @@ theorem of_injective : Function.Injective (@of α) :=
 #align free_add_monoid.of_injective FreeAddMonoid.of_injective
 -/
 
-/- warning: free_monoid.rec_on -> FreeMonoid.recOn is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {C : (FreeMonoid.{u1} α) -> Sort.{u2}} (xs : FreeMonoid.{u1} α), (C (OfNat.ofNat.{u1} (FreeMonoid.{u1} α) 1 (OfNat.mk.{u1} (FreeMonoid.{u1} α) 1 (One.one.{u1} (FreeMonoid.{u1} α) (MulOneClass.toHasOne.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α))))))))) -> (forall (x : α) (xs : FreeMonoid.{u1} α), (C xs) -> (C (HMul.hMul.{u1, u1, u1} (FreeMonoid.{u1} α) (FreeMonoid.{u1} α) (FreeMonoid.{u1} α) (instHMul.{u1} (FreeMonoid.{u1} α) (MulOneClass.toHasMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))))) (FreeMonoid.of.{u1} α x) xs))) -> (C xs)
-but is expected to have type
-  forall {α : Type.{u1}} {C : (FreeMonoid.{u1} α) -> Sort.{u2}} (xs : FreeMonoid.{u1} α), (C (OfNat.ofNat.{u1} (FreeMonoid.{u1} α) 1 (One.toOfNat1.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toOne.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))))) -> (forall (x : α) (xs : FreeMonoid.{u1} α), (C xs) -> (C (HMul.hMul.{u1, u1, u1} (FreeMonoid.{u1} α) (FreeMonoid.{u1} α) (FreeMonoid.{u1} α) (instHMul.{u1} (FreeMonoid.{u1} α) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))))) (FreeMonoid.of.{u1} α x) xs))) -> (C xs)
-Case conversion may be inaccurate. Consider using '#align free_monoid.rec_on FreeMonoid.recOnₓ'. -/
 /-- Recursor for `free_monoid` using `1` and `free_monoid.of x * xs` instead of `[]` and
 `x :: xs`. -/
 @[elab_as_elim,
@@ -238,12 +232,6 @@ def recOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
 #align free_monoid.rec_on FreeMonoid.recOn
 #align free_add_monoid.rec_on FreeAddMonoid.recOn
 
-/- warning: free_monoid.rec_on_one -> FreeMonoid.recOn_one is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align free_monoid.rec_on_one FreeMonoid.recOn_oneₓ'. -/
 @[simp, to_additive]
 theorem recOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C xs → C (of x * xs)) :
     @recOn α C 1 h0 ih = h0 :=
@@ -251,12 +239,6 @@ theorem recOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C xs
 #align free_monoid.rec_on_one FreeMonoid.recOn_one
 #align free_add_monoid.rec_on_zero FreeAddMonoid.recOn_zero
 
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-Case conversion may be inaccurate. Consider using '#align free_monoid.rec_on_of_mul FreeMonoid.recOn_of_mulₓ'. -/
 @[simp, to_additive]
 theorem recOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C xs → C (of x * xs)) : @recOn α C (of x * xs) h0 ih = ih x xs (recOn xs h0 ih) :=
@@ -264,12 +246,6 @@ theorem recOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α
 #align free_monoid.rec_on_of_mul FreeMonoid.recOn_of_mul
 #align free_add_monoid.rec_on_of_add FreeAddMonoid.recOn_of_add
 
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-Case conversion may be inaccurate. Consider using '#align free_monoid.cases_on FreeMonoid.casesOnₓ'. -/
 /-- A version of `list.cases_on` for `free_monoid` using `1` and `free_monoid.of x * xs` instead of
 `[]` and `x :: xs`. -/
 @[elab_as_elim,
@@ -281,12 +257,6 @@ def casesOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
 #align free_monoid.cases_on FreeMonoid.casesOn
 #align free_add_monoid.cases_on FreeAddMonoid.casesOn
 
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-Case conversion may be inaccurate. Consider using '#align free_monoid.cases_on_one FreeMonoid.casesOn_oneₓ'. -/
 @[simp, to_additive]
 theorem casesOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C (of x * xs)) :
     @casesOn α C 1 h0 ih = h0 :=
@@ -294,12 +264,6 @@ theorem casesOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C
 #align free_monoid.cases_on_one FreeMonoid.casesOn_one
 #align free_add_monoid.cases_on_zero FreeAddMonoid.casesOn_zero
 
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 @[simp, to_additive]
 theorem casesOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C (of x * xs)) : @casesOn α C (of x * xs) h0 ih = ih x xs :=
@@ -307,12 +271,6 @@ theorem casesOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid
 #align free_monoid.cases_on_of_mul FreeMonoid.casesOn_of_mul
 #align free_add_monoid.cases_on_of_add FreeAddMonoid.casesOn_of_add
 
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 @[ext, to_additive]
 theorem hom_eq ⦃f g : FreeMonoid α →* M⦄ (h : ∀ x, f (of x) = g (of x)) : f = g :=
   MonoidHom.ext fun l =>
@@ -333,12 +291,6 @@ def prodAux {M} [Monoid M] (l : List M) : M :=
 #align free_add_monoid.sum_aux FreeAddMonoid.sumAux
 -/
 
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 @[to_additive]
 theorem prodAux_eq : ∀ l : List M, FreeMonoid.prodAux l = l.Prod
   | [] => rfl
@@ -346,12 +298,6 @@ theorem prodAux_eq : ∀ l : List M, FreeMonoid.prodAux l = l.Prod
 #align free_monoid.prod_aux_eq FreeMonoid.prodAux_eq
 #align free_add_monoid.sum_aux_eq FreeAddMonoid.sumAux_eq
 
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 /-- Equivalence between maps `α → M` and monoid homomorphisms `free_monoid α →* M`. -/
 @[to_additive
       "Equivalence between maps `α → A` and additive monoid homomorphisms\n`free_add_monoid α →+ A`."]
@@ -366,92 +312,47 @@ def lift : (α → M) ≃ (FreeMonoid α →* M)
 #align free_monoid.lift FreeMonoid.lift
 #align free_add_monoid.lift FreeAddMonoid.lift
 
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 @[simp, to_additive]
 theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of :=
   rfl
 #align free_monoid.lift_symm_apply FreeMonoid.lift_symm_apply
 #align free_add_monoid.lift_symm_apply FreeAddMonoid.lift_symm_apply
 
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 @[to_additive]
 theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = (l.toList.map f).Prod :=
   prodAux_eq _
 #align free_monoid.lift_apply FreeMonoid.lift_apply
 #align free_add_monoid.lift_apply FreeAddMonoid.lift_apply
 
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 @[to_additive]
 theorem lift_comp_of (f : α → M) : lift f ∘ of = f :=
   rfl
 #align free_monoid.lift_comp_of FreeMonoid.lift_comp_of
 #align free_add_monoid.lift_comp_of FreeAddMonoid.lift_comp_of
 
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 @[simp, to_additive]
 theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x :=
   rfl
 #align free_monoid.lift_eval_of FreeMonoid.lift_eval_of
 #align free_add_monoid.lift_eval_of FreeAddMonoid.lift_eval_of
 
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 @[simp, to_additive]
 theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f :=
   lift.apply_symm_apply f
 #align free_monoid.lift_restrict FreeMonoid.lift_restrict
 #align free_add_monoid.lift_restrict FreeAddMonoid.lift_restrict
 
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 @[to_additive]
 theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) := by ext; simp
 #align free_monoid.comp_lift FreeMonoid.comp_lift
 #align free_add_monoid.comp_lift FreeAddMonoid.comp_lift
 
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 @[to_additive]
 theorem hom_map_lift (g : M →* N) (f : α → M) (x : FreeMonoid α) : g (lift f x) = lift (g ∘ f) x :=
   MonoidHom.ext_iff.1 (comp_lift g f) x
 #align free_monoid.hom_map_lift FreeMonoid.hom_map_lift
 #align free_add_monoid.hom_map_lift FreeAddMonoid.hom_map_lift
 
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 /-- Define a multiplicative action of `free_monoid α` on `β`. -/
 @[to_additive "Define an additive action of `free_add_monoid α` on `β`."]
 def mkMulAction (f : α → β → β) : MulAction (FreeMonoid α) β
@@ -462,12 +363,6 @@ def mkMulAction (f : α → β → β) : MulAction (FreeMonoid α) β
 #align free_monoid.mk_mul_action FreeMonoid.mkMulAction
 #align free_add_monoid.mk_add_action FreeAddMonoid.mkAddAction
 
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 @[to_additive]
 theorem smul_def (f : α → β → β) (l : FreeMonoid α) (b : β) :
     haveI := mk_mul_action f
@@ -476,12 +371,6 @@ theorem smul_def (f : α → β → β) (l : FreeMonoid α) (b : β) :
 #align free_monoid.smul_def FreeMonoid.smul_def
 #align free_add_monoid.vadd_def FreeAddMonoid.vadd_def
 
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 @[to_additive]
 theorem ofList_smul (f : α → β → β) (l : List α) (b : β) :
     haveI := mk_mul_action f
@@ -501,12 +390,6 @@ theorem of_smul (f : α → β → β) (x : α) (y : β) :
 #align free_add_monoid.of_vadd FreeAddMonoid.of_vadd
 -/
 
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 /-- The unique monoid homomorphism `free_monoid α →* free_monoid β` that sends
 each `of x` to `of (f x)`. -/
 @[to_additive
@@ -519,72 +402,36 @@ def map (f : α → β) : FreeMonoid α →* FreeMonoid β
 #align free_monoid.map FreeMonoid.map
 #align free_add_monoid.map FreeAddMonoid.map
 
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 @[simp, to_additive]
 theorem map_of (f : α → β) (x : α) : map f (of x) = of (f x) :=
   rfl
 #align free_monoid.map_of FreeMonoid.map_of
 #align free_add_monoid.map_of FreeAddMonoid.map_of
 
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 @[to_additive]
 theorem toList_map (f : α → β) (xs : FreeMonoid α) : (map f xs).toList = xs.toList.map f :=
   rfl
 #align free_monoid.to_list_map FreeMonoid.toList_map
 #align free_add_monoid.to_list_map FreeAddMonoid.toList_map
 
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 @[to_additive]
 theorem ofList_map (f : α → β) (xs : List α) : ofList (xs.map f) = map f (ofList xs) :=
   rfl
 #align free_monoid.of_list_map FreeMonoid.ofList_map
 #align free_add_monoid.of_list_map FreeAddMonoid.ofList_map
 
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 @[to_additive]
 theorem lift_of_comp_eq_map (f : α → β) : (lift fun x => of (f x)) = map f :=
   hom_eq fun x => rfl
 #align free_monoid.lift_of_comp_eq_map FreeMonoid.lift_of_comp_eq_map
 #align free_add_monoid.lift_of_comp_eq_map FreeAddMonoid.lift_of_comp_eq_map
 
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 @[to_additive]
 theorem map_comp (g : β → γ) (f : α → β) : map (g ∘ f) = (map g).comp (map f) :=
   hom_eq fun x => rfl
 #align free_monoid.map_comp FreeMonoid.map_comp
 #align free_add_monoid.map_comp FreeAddMonoid.map_comp
 
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 @[simp, to_additive]
 theorem map_id : map (@id α) = MonoidHom.id (FreeMonoid α) :=
   hom_eq fun x => rfl

657df433

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -433,10 +433,7 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.comp_lift FreeMonoid.comp_liftₓ'. -/
 @[to_additive]
-theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) :=
-  by
-  ext
-  simp
+theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) := by ext; simp
 #align free_monoid.comp_lift FreeMonoid.comp_lift
 #align free_add_monoid.comp_lift FreeAddMonoid.comp_lift

657df433

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -441,10 +441,7 @@ theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘
 #align free_add_monoid.comp_lift FreeAddMonoid.comp_lift
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align free_monoid.hom_map_lift FreeMonoid.hom_map_liftₓ'. -/
 @[to_additive]
 theorem hom_map_lift (g : M →* N) (f : α → M) (x : FreeMonoid α) : g (lift f x) = lift (g ∘ f) x :=

657df433

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -311,7 +311,7 @@ theorem casesOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid
 lean 3 declaration is
   forall {α : Type.{u1}} {M : Type.{u2}} [_inst_1 : Monoid.{u2} M] {{f : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)}} {{g : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)}}, (forall (x : α), Eq.{succ u2} M (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) => (FreeMonoid.{u1} α) -> M) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) f (FreeMonoid.of.{u1} α x)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) => (FreeMonoid.{u1} α) -> M) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) g (FreeMonoid.of.{u1} α x))) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) f g)
 but is expected to have type
-  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {{f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}} {{g : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}}, (forall (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) g (FreeMonoid.of.{u2} α x))) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f g)
+  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {{f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}} {{g : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}}, (forall (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u2} α) => M) (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) g (FreeMonoid.of.{u2} α x))) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f g)
 Case conversion may be inaccurate. Consider using '#align free_monoid.hom_eq FreeMonoid.hom_eqₓ'. -/
 @[ext, to_additive]
 theorem hom_eq ⦃f g : FreeMonoid α →* M⦄ (h : ∀ x, f (of x) = g (of x)) : f = g :=
@@ -370,7 +370,7 @@ def lift : (α → M) ≃ (FreeMonoid α →* M)
 lean 3 declaration is
   forall {α : Type.{u1}} {M : Type.{u2}} [_inst_1 : Monoid.{u2} M] (f : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)), Eq.{max (succ u1) (succ u2)} (α -> M) (coeFn.{max 1 (max (max (succ u2) (succ u1)) (succ u1) (succ u2)) (max (succ u1) (succ u2)) (succ u2) (succ u1), max (max (succ u2) (succ u1)) (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (α -> M)) (fun (_x : Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (α -> M)) => (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) -> α -> M) (Equiv.hasCoeToFun.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (α -> M)) (Equiv.symm.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (α -> M) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (FreeMonoid.lift.{u1, u2} α M _inst_1)) f) (Function.comp.{succ u1, succ u1, succ u2} α (FreeMonoid.{u1} α) M (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) => (FreeMonoid.{u1} α) -> M) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) f) (FreeMonoid.of.{u1} α))
 but is expected to have type
-  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) f) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (α -> M)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (α -> M)) (Equiv.symm.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.lift.{u2, u1} α M _inst_1)) f) (Function.comp.{succ u2, succ u2, succ u1} α (FreeMonoid.{u2} α) M (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f) (FreeMonoid.of.{u2} α))
+  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) f) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (α -> M)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (α -> M)) (Equiv.symm.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.lift.{u2, u1} α M _inst_1)) f) (Function.comp.{succ u2, succ u2, succ u1} α (FreeMonoid.{u2} α) M (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f) (FreeMonoid.of.{u2} α))
 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_symm_apply FreeMonoid.lift_symm_applyₓ'. -/
 @[simp, to_additive]
 theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of :=
@@ -382,7 +382,7 @@ theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of :=
 lean 3 declaration is
   forall {α : Type.{u1}} {M : Type.{u2}} [_inst_1 : Monoid.{u2} M] (f : α -> M) (l : FreeMonoid.{u1} α), Eq.{succ u2} M (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) => (FreeMonoid.{u1} α) -> M) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (coeFn.{max 1 (max (max (succ u1) (succ u2)) (succ u2) (succ u1)) (max (succ u2) (succ u1)) (succ u1) (succ u2), max (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (α -> M) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1))) (fun (_x : Equiv.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (α -> M) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1))) => (α -> M) -> (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1))) (Equiv.hasCoeToFun.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (α -> M) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1))) (FreeMonoid.lift.{u1, u2} α M _inst_1) f) l) (List.prod.{u2} M (MulOneClass.toHasMul.{u2} M (Monoid.toMulOneClass.{u2} M _inst_1)) (MulOneClass.toHasOne.{u2} M (Monoid.toMulOneClass.{u2} M _inst_1)) (List.map.{u1, u2} α M f (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (FreeMonoid.{u1} α) (List.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} (FreeMonoid.{u1} α) (List.{u1} α)) => (FreeMonoid.{u1} α) -> (List.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} (FreeMonoid.{u1} α) (List.{u1} α)) (FreeMonoid.toList.{u1} α) l)))
 but is expected to have type
-  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : α -> M) (l : FreeMonoid.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) l) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1))) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1))) (FreeMonoid.lift.{u2, u1} α M _inst_1) f) l) (List.prod.{u1} M (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Monoid.toOne.{u1} M _inst_1) (List.map.{u2, u1} α M f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) l)))
+  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : α -> M) (l : FreeMonoid.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u2} α) => M) l) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1))) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1))) (FreeMonoid.lift.{u2, u1} α M _inst_1) f) l) (List.prod.{u1} M (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Monoid.toOne.{u1} M _inst_1) (List.map.{u2, u1} α M f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) l)))
 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_apply FreeMonoid.lift_applyₓ'. -/
 @[to_additive]
 theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = (l.toList.map f).Prod :=
@@ -394,7 +394,7 @@ theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = (l.toList.map
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_comp_of FreeMonoid.lift_comp_ofₓ'. -/
 @[to_additive]
 theorem lift_comp_of (f : α → M) : lift f ∘ of = f :=
@@ -406,7 +406,7 @@ theorem lift_comp_of (f : α → M) : lift f ∘ of = f :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_eval_of FreeMonoid.lift_eval_ofₓ'. -/
 @[simp, to_additive]
 theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x :=
@@ -418,7 +418,7 @@ theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_restrict FreeMonoid.lift_restrictₓ'. -/
 @[simp, to_additive]
 theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f :=
@@ -430,7 +430,7 @@ theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.comp_lift FreeMonoid.comp_liftₓ'. -/
 @[to_additive]
 theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) :=
@@ -444,7 +444,7 @@ theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘
 lean 3 declaration is
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(FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)) (Function.comp.{succ u1, succ u3, succ u2} α M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)))) g) f)) (FreeMonoid.{u1} α) N (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α))))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α -> N) => MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)) (Function.comp.{succ u1, succ u3, succ u2} α M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)))) g) f)) (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (α -> N) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2))) (α -> N) (fun (_x : α -> N) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α -> N) => MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (α -> N) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2))) (FreeMonoid.lift.{u1, u2} α N _inst_2) (Function.comp.{succ u1, succ u3, succ u2} α M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : M) => N) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)))) g) f)) x)
 Case conversion may be inaccurate. Consider using '#align free_monoid.hom_map_lift FreeMonoid.hom_map_liftₓ'. -/
 @[to_additive]
 theorem hom_map_lift (g : M →* N) (f : α → M) (x : FreeMonoid α) : g (lift f x) = lift (g ∘ f) x :=
@@ -472,7 +472,7 @@ def mkMulAction (f : α → β → β) : MulAction (FreeMonoid α) β
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β -> β) (l : FreeMonoid.{u1} α) (b : β), Eq.{succ u2} β (SMul.smul.{u1, u2} (FreeMonoid.{u1} α) β (MulAction.toHasSmul.{u1, u2} (FreeMonoid.{u1} α) β (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α))) (FreeMonoid.mkMulAction.{u1, u2} α β f)) l b) (List.foldr.{u1, u2} α β f b (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (FreeMonoid.{u1} α) (List.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} (FreeMonoid.{u1} α) (List.{u1} α)) => (FreeMonoid.{u1} α) -> (List.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} (FreeMonoid.{u1} α) (List.{u1} α)) (FreeMonoid.toList.{u1} α) l))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β -> β) (l : FreeMonoid.{u2} α) (b : β), Eq.{succ u1} β (HSMul.hSMul.{u2, u1, u1} (FreeMonoid.{u2} α) β β (instHSMul.{u2, u1} (FreeMonoid.{u2} α) β (MulAction.toSMul.{u2, u1} (FreeMonoid.{u2} α) β (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))) (FreeMonoid.mkMulAction.{u2, u1} α β f))) l b) (List.foldr.{u2, u1} α β f b (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) l))
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β -> β) (l : FreeMonoid.{u2} α) (b : β), Eq.{succ u1} β (HSMul.hSMul.{u2, u1, u1} (FreeMonoid.{u2} α) β β (instHSMul.{u2, u1} (FreeMonoid.{u2} α) β (MulAction.toSMul.{u2, u1} (FreeMonoid.{u2} α) β (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))) (FreeMonoid.mkMulAction.{u2, u1} α β f))) l b) (List.foldr.{u2, u1} α β f b (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) l))
 Case conversion may be inaccurate. Consider using '#align free_monoid.smul_def FreeMonoid.smul_defₓ'. -/
 @[to_additive]
 theorem smul_def (f : α → β → β) (l : FreeMonoid α) (b : β) :
@@ -486,7 +486,7 @@ theorem smul_def (f : α → β → β) (l : FreeMonoid α) (b : β) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β -> β) (l : List.{u1} α) (b : β), Eq.{succ u2} β (SMul.smul.{u1, u2} (FreeMonoid.{u1} α) β (MulAction.toHasSmul.{u1, u2} (FreeMonoid.{u1} α) β (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α))) (FreeMonoid.mkMulAction.{u1, u2} α β f)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (List.{u1} α) (FreeMonoid.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} (List.{u1} α) (FreeMonoid.{u1} α)) => (List.{u1} α) -> (FreeMonoid.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} (List.{u1} α) (FreeMonoid.{u1} α)) (FreeMonoid.ofList.{u1} α) l) b) (List.foldr.{u1, u2} α β f b l)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β -> β) (l : List.{u2} α) (b : β), Eq.{succ u1} β (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) β β (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) β (MulAction.toSMul.{u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) β (RightCancelMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) (CancelMonoid.toRightCancelMonoid.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))) (FreeMonoid.mkMulAction.{u2, u1} α β f))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (List.{u2} α) (fun (_x : List.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (FreeMonoid.ofList.{u2} α) l) b) (List.foldr.{u2, u1} α β f b l)
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β -> β) (l : List.{u2} α) (b : β), Eq.{succ u1} β (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : List.{u2} α) => FreeMonoid.{u2} α) l) β β (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : List.{u2} α) => FreeMonoid.{u2} α) l) β (MulAction.toSMul.{u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : List.{u2} α) => FreeMonoid.{u2} α) l) β (RightCancelMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : List.{u2} α) => FreeMonoid.{u2} α) l) (CancelMonoid.toRightCancelMonoid.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : List.{u2} α) => FreeMonoid.{u2} α) l) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))) (FreeMonoid.mkMulAction.{u2, u1} α β f))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (List.{u2} α) (fun (_x : List.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : List.{u2} α) => FreeMonoid.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (FreeMonoid.ofList.{u2} α) l) b) (List.foldr.{u2, u1} α β f b l)
 Case conversion may be inaccurate. Consider using '#align free_monoid.of_list_smul FreeMonoid.ofList_smulₓ'. -/
 @[to_additive]
 theorem ofList_smul (f : α → β → β) (l : List α) (b : β) :
@@ -529,7 +529,7 @@ def map (f : α → β) : FreeMonoid α →* FreeMonoid β
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (x : α), Eq.{succ u2} (FreeMonoid.{u2} β) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) => (FreeMonoid.{u1} α) -> (FreeMonoid.{u2} β)) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) (FreeMonoid.map.{u1, u2} α β f) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u2} β (f x))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) (FreeMonoid.of.{u1} α x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (fun (_x : FreeMonoid.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α))))) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))))) (FreeMonoid.map.{u1, u2} α β f) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u2} β (f x))
+  forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) (FreeMonoid.of.{u1} α x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (fun (_x : FreeMonoid.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α))))) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))))) (FreeMonoid.map.{u1, u2} α β f) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u2} β (f x))
 Case conversion may be inaccurate. Consider using '#align free_monoid.map_of FreeMonoid.map_ofₓ'. -/
 @[simp, to_additive]
 theorem map_of (f : α → β) (x : α) : map f (of x) = of (f x) :=
@@ -541,7 +541,7 @@ theorem map_of (f : α → β) (x : α) : map f (of x) = of (f x) :=
 lean 3 declaration is
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 but is expected to have type
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(RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => FreeMonoid.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))))) (FreeMonoid.map.{u2, u1} α β f) xs)) (List.map.{u2, u1} α β f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) xs))
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (xs : FreeMonoid.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : FreeMonoid.{u1} β) => List.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (fun (a : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u2} α) => FreeMonoid.{u1} β) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} 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(FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))))) (FreeMonoid.map.{u2, u1} α β f) xs)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (FreeMonoid.{u1} β) (List.{u1} β)) (FreeMonoid.{u1} β) (fun (_x : FreeMonoid.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : FreeMonoid.{u1} β) => List.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (FreeMonoid.{u1} β) (List.{u1} β)) (FreeMonoid.toList.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : FreeMonoid.{u2} α) => FreeMonoid.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))))) (FreeMonoid.map.{u2, u1} α β f) xs)) (List.map.{u2, u1} α β f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) xs))
 Case conversion may be inaccurate. Consider using '#align free_monoid.to_list_map FreeMonoid.toList_mapₓ'. -/
 @[to_additive]
 theorem toList_map (f : α → β) (xs : FreeMonoid α) : (map f xs).toList = xs.toList.map f :=
@@ -553,7 +553,7 @@ theorem toList_map (f : α → β) (xs : FreeMonoid α) : (map f xs).toList = xs
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.of_list_map FreeMonoid.ofList_mapₓ'. -/
 @[to_additive]
 theorem ofList_map (f : α → β) (xs : List α) : ofList (xs.map f) = map f (ofList xs) :=
@@ -565,7 +565,7 @@ theorem ofList_map (f : α → β) (xs : List α) : ofList (xs.map f) = map f (o
 lean 3 declaration is
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 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> (FreeMonoid.{u1} β)) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (fun (x : α) => FreeMonoid.of.{u1} β (f x))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (α -> (FreeMonoid.{u1} β)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))))) (α -> (FreeMonoid.{u1} β)) (fun (_x : α -> (FreeMonoid.{u1} β)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> (FreeMonoid.{u1} β)) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> (FreeMonoid.{u1} β)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))))) (FreeMonoid.lift.{u2, u1} α (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (fun (x : α) => FreeMonoid.of.{u1} β (f x))) (FreeMonoid.map.{u2, u1} α β f)
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α -> (FreeMonoid.{u1} β)) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (fun (x : α) => FreeMonoid.of.{u1} β (f x))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (α -> (FreeMonoid.{u1} β)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))))) (α -> (FreeMonoid.{u1} β)) (fun (_x : α -> (FreeMonoid.{u1} β)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α -> (FreeMonoid.{u1} β)) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> (FreeMonoid.{u1} β)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))))) (FreeMonoid.lift.{u2, u1} α (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (fun (x : α) => FreeMonoid.of.{u1} β (f x))) (FreeMonoid.map.{u2, u1} α β f)
 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_of_comp_eq_map FreeMonoid.lift_of_comp_eq_mapₓ'. -/
 @[to_additive]
 theorem lift_of_comp_eq_map (f : α → β) : (lift fun x => of (f x)) = map f :=

657df433

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -311,7 +311,7 @@ theorem casesOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid
 lean 3 declaration is
   forall {α : Type.{u1}} {M : Type.{u2}} [_inst_1 : Monoid.{u2} M] {{f : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)}} {{g : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)}}, (forall (x : α), Eq.{succ u2} M (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) => (FreeMonoid.{u1} α) -> M) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) f (FreeMonoid.of.{u1} α x)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) => (FreeMonoid.{u1} α) -> M) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) g (FreeMonoid.of.{u1} α x))) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) f g)
 but is expected to have type
-  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {{f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}} {{g : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}}, (forall (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => M) (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) g (FreeMonoid.of.{u2} α x))) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f g)
+  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {{f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}} {{g : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}}, (forall (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) g (FreeMonoid.of.{u2} α x))) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f g)
 Case conversion may be inaccurate. Consider using '#align free_monoid.hom_eq FreeMonoid.hom_eqₓ'. -/
 @[ext, to_additive]
 theorem hom_eq ⦃f g : FreeMonoid α →* M⦄ (h : ∀ x, f (of x) = g (of x)) : f = g :=
@@ -370,7 +370,7 @@ def lift : (α → M) ≃ (FreeMonoid α →* M)
 lean 3 declaration is
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 but is expected to have type
-  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) f) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) 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(CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (α -> M)) (Equiv.symm.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.lift.{u2, u1} α M _inst_1)) f) (Function.comp.{succ u2, succ u2, succ u1} α (FreeMonoid.{u2} α) M (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f) (FreeMonoid.of.{u2} α))
+  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) f) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) 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(CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (α -> M)) (Equiv.symm.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.lift.{u2, u1} α M _inst_1)) f) (Function.comp.{succ u2, succ u2, succ u1} α (FreeMonoid.{u2} α) M (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f) (FreeMonoid.of.{u2} α))
 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_symm_apply FreeMonoid.lift_symm_applyₓ'. -/
 @[simp, to_additive]
 theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of :=
@@ -382,7 +382,7 @@ theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_apply FreeMonoid.lift_applyₓ'. -/
 @[to_additive]
 theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = (l.toList.map f).Prod :=
@@ -394,7 +394,7 @@ theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = (l.toList.map
 lean 3 declaration is
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 but is expected to have type
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+  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : α -> M), Eq.{max (succ u2) (succ u1)} (α -> M) (Function.comp.{succ u2, succ u2, succ u1} α (FreeMonoid.{u2} α) M (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1))) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1))) (FreeMonoid.lift.{u2, u1} α M _inst_1) f)) (FreeMonoid.of.{u2} α)) f
 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_comp_of FreeMonoid.lift_comp_ofₓ'. -/
 @[to_additive]
 theorem lift_comp_of (f : α → M) : lift f ∘ of = f :=
@@ -406,7 +406,7 @@ theorem lift_comp_of (f : α → M) : lift f ∘ of = f :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_eval_of FreeMonoid.lift_eval_ofₓ'. -/
 @[simp, to_additive]
 theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x :=
@@ -418,7 +418,7 @@ theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_restrict FreeMonoid.lift_restrictₓ'. -/
 @[simp, to_additive]
 theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f :=
@@ -430,7 +430,7 @@ theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.comp_lift FreeMonoid.comp_liftₓ'. -/
 @[to_additive]
 theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) :=
@@ -444,7 +444,7 @@ theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘
 lean 3 declaration is
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(FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)) (Function.comp.{succ u1, succ u3, succ u2} α M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)))) g) f)) (FreeMonoid.{u1} α) N (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α))))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> N) => MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)) (Function.comp.{succ u1, succ u3, succ u2} α M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)))) g) f)) (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (α -> N) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2))) (α -> N) (fun (_x : α -> N) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> N) => MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (α -> N) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2))) (FreeMonoid.lift.{u1, u2} α N _inst_2) (Function.comp.{succ u1, succ u3, succ u2} α M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : M) => N) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)))) g) f)) x)
 Case conversion may be inaccurate. Consider using '#align free_monoid.hom_map_lift FreeMonoid.hom_map_liftₓ'. -/
 @[to_additive]
 theorem hom_map_lift (g : M →* N) (f : α → M) (x : FreeMonoid α) : g (lift f x) = lift (g ∘ f) x :=
@@ -472,7 +472,7 @@ def mkMulAction (f : α → β → β) : MulAction (FreeMonoid α) β
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β -> β) (l : FreeMonoid.{u1} α) (b : β), Eq.{succ u2} β (SMul.smul.{u1, u2} (FreeMonoid.{u1} α) β (MulAction.toHasSmul.{u1, u2} (FreeMonoid.{u1} α) β (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α))) (FreeMonoid.mkMulAction.{u1, u2} α β f)) l b) (List.foldr.{u1, u2} α β f b (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (FreeMonoid.{u1} α) (List.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} (FreeMonoid.{u1} α) (List.{u1} α)) => (FreeMonoid.{u1} α) -> (List.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} (FreeMonoid.{u1} α) (List.{u1} α)) (FreeMonoid.toList.{u1} α) l))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β -> β) (l : FreeMonoid.{u2} α) (b : β), Eq.{succ u1} β (HSMul.hSMul.{u2, u1, u1} (FreeMonoid.{u2} α) β β (instHSMul.{u2, u1} (FreeMonoid.{u2} α) β (MulAction.toSMul.{u2, u1} (FreeMonoid.{u2} α) β (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))) (FreeMonoid.mkMulAction.{u2, u1} α β f))) l b) (List.foldr.{u2, u1} α β f b (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) l))
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β -> β) (l : FreeMonoid.{u2} α) (b : β), Eq.{succ u1} β (HSMul.hSMul.{u2, u1, u1} (FreeMonoid.{u2} α) β β (instHSMul.{u2, u1} (FreeMonoid.{u2} α) β (MulAction.toSMul.{u2, u1} (FreeMonoid.{u2} α) β (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))) (FreeMonoid.mkMulAction.{u2, u1} α β f))) l b) (List.foldr.{u2, u1} α β f b (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) l))
 Case conversion may be inaccurate. Consider using '#align free_monoid.smul_def FreeMonoid.smul_defₓ'. -/
 @[to_additive]
 theorem smul_def (f : α → β → β) (l : FreeMonoid α) (b : β) :
@@ -486,7 +486,7 @@ theorem smul_def (f : α → β → β) (l : FreeMonoid α) (b : β) :
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β -> β) (l : List.{u1} α) (b : β), Eq.{succ u2} β (SMul.smul.{u1, u2} (FreeMonoid.{u1} α) β (MulAction.toHasSmul.{u1, u2} (FreeMonoid.{u1} α) β (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α))) (FreeMonoid.mkMulAction.{u1, u2} α β f)) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (List.{u1} α) (FreeMonoid.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} (List.{u1} α) (FreeMonoid.{u1} α)) => (List.{u1} α) -> (FreeMonoid.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} (List.{u1} α) (FreeMonoid.{u1} α)) (FreeMonoid.ofList.{u1} α) l) b) (List.foldr.{u1, u2} α β f b l)
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β -> β) (l : List.{u2} α) (b : β), Eq.{succ u1} β (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u2} α) => FreeMonoid.{u2} α) l) β β (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u2} α) => FreeMonoid.{u2} α) l) β (MulAction.toSMul.{u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u2} α) => FreeMonoid.{u2} α) l) β (RightCancelMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u2} α) => FreeMonoid.{u2} α) l) (CancelMonoid.toRightCancelMonoid.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u2} α) => FreeMonoid.{u2} α) l) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))) (FreeMonoid.mkMulAction.{u2, u1} α β f))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (List.{u2} α) (fun (_x : List.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u2} α) => FreeMonoid.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (FreeMonoid.ofList.{u2} α) l) b) (List.foldr.{u2, u1} α β f b l)
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β -> β) (l : List.{u2} α) (b : β), Eq.{succ u1} β (HSMul.hSMul.{u2, u1, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) β β (instHSMul.{u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) β (MulAction.toSMul.{u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) β (RightCancelMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) (CancelMonoid.toRightCancelMonoid.{u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) l) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))) (FreeMonoid.mkMulAction.{u2, u1} α β f))) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (List.{u2} α) (fun (_x : List.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : List.{u2} α) => FreeMonoid.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (FreeMonoid.ofList.{u2} α) l) b) (List.foldr.{u2, u1} α β f b l)
 Case conversion may be inaccurate. Consider using '#align free_monoid.of_list_smul FreeMonoid.ofList_smulₓ'. -/
 @[to_additive]
 theorem ofList_smul (f : α → β → β) (l : List α) (b : β) :
@@ -529,7 +529,7 @@ def map (f : α → β) : FreeMonoid α →* FreeMonoid β
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (x : α), Eq.{succ u2} (FreeMonoid.{u2} β) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) => (FreeMonoid.{u1} α) -> (FreeMonoid.{u2} β)) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) (FreeMonoid.map.{u1, u2} α β f) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u2} β (f x))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) (FreeMonoid.of.{u1} α x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (fun (_x : FreeMonoid.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α))))) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))))) (FreeMonoid.map.{u1, u2} α β f) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u2} β (f x))
+  forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) (FreeMonoid.of.{u1} α x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (fun (_x : FreeMonoid.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α))))) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))))) (FreeMonoid.map.{u1, u2} α β f) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u2} β (f x))
 Case conversion may be inaccurate. Consider using '#align free_monoid.map_of FreeMonoid.map_ofₓ'. -/
 @[simp, to_additive]
 theorem map_of (f : α → β) (x : α) : map f (of x) = of (f x) :=
@@ -541,7 +541,7 @@ theorem map_of (f : α → β) (x : α) : map f (of x) = of (f x) :=
 lean 3 declaration is
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 but is expected to have type
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(FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))))) (FreeMonoid.map.{u2, u1} α β f) xs)) (List.map.{u2, u1} α β f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) xs))
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (xs : FreeMonoid.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : FreeMonoid.{u1} β) => List.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (fun (a : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => FreeMonoid.{u1} β) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))))) (FreeMonoid.map.{u2, u1} α β f) xs)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (FreeMonoid.{u1} β) (List.{u1} β)) (FreeMonoid.{u1} β) (fun (_x : FreeMonoid.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : FreeMonoid.{u1} β) => List.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (FreeMonoid.{u1} β) (List.{u1} β)) (FreeMonoid.toList.{u1} β) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : FreeMonoid.{u2} α) => FreeMonoid.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))))) (FreeMonoid.map.{u2, u1} α β f) xs)) (List.map.{u2, u1} α β f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) xs))
 Case conversion may be inaccurate. Consider using '#align free_monoid.to_list_map FreeMonoid.toList_mapₓ'. -/
 @[to_additive]
 theorem toList_map (f : α → β) (xs : FreeMonoid α) : (map f xs).toList = xs.toList.map f :=
@@ -553,7 +553,7 @@ theorem toList_map (f : α → β) (xs : FreeMonoid α) : (map f xs).toList = xs
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.of_list_map FreeMonoid.ofList_mapₓ'. -/
 @[to_additive]
 theorem ofList_map (f : α → β) (xs : List α) : ofList (xs.map f) = map f (ofList xs) :=
@@ -565,7 +565,7 @@ theorem ofList_map (f : α → β) (xs : List α) : ofList (xs.map f) = map f (o
 lean 3 declaration is
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 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α -> (FreeMonoid.{u1} β)) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (fun (x : α) => FreeMonoid.of.{u1} β (f x))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (α -> (FreeMonoid.{u1} β)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))))) (α -> (FreeMonoid.{u1} β)) (fun (_x : α -> (FreeMonoid.{u1} β)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α -> (FreeMonoid.{u1} β)) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> (FreeMonoid.{u1} β)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))))) (FreeMonoid.lift.{u2, u1} α (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (fun (x : α) => FreeMonoid.of.{u1} β (f x))) (FreeMonoid.map.{u2, u1} α β f)
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> (FreeMonoid.{u1} β)) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (fun (x : α) => FreeMonoid.of.{u1} β (f x))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (α -> (FreeMonoid.{u1} β)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))))) (α -> (FreeMonoid.{u1} β)) (fun (_x : α -> (FreeMonoid.{u1} β)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α -> (FreeMonoid.{u1} β)) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> (FreeMonoid.{u1} β)) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))))) (FreeMonoid.lift.{u2, u1} α (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (fun (x : α) => FreeMonoid.of.{u1} β (f x))) (FreeMonoid.map.{u2, u1} α β f)
 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_of_comp_eq_map FreeMonoid.lift_of_comp_eq_mapₓ'. -/
 @[to_additive]
 theorem lift_of_comp_eq_map (f : α → β) : (lift fun x => of (f x)) = map f :=

657df433

bump to nightly-2023-03-08-18

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

10f15343

Diff

@@ -311,7 +311,7 @@ theorem casesOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid
 lean 3 declaration is
   forall {α : Type.{u1}} {M : Type.{u2}} [_inst_1 : Monoid.{u2} M] {{f : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)}} {{g : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)}}, (forall (x : α), Eq.{succ u2} M (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) => (FreeMonoid.{u1} α) -> M) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) f (FreeMonoid.of.{u1} α x)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) => (FreeMonoid.{u1} α) -> M) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) g (FreeMonoid.of.{u1} α x))) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) M (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} M _inst_1)) f g)
 but is expected to have type
-  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {{f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}} {{g : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}}, (forall (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : FreeMonoid.{u2} α) => M) (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) g (FreeMonoid.of.{u2} α x))) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f g)
+  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {{f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}} {{g : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)}}, (forall (x : α), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => M) (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f (FreeMonoid.of.{u2} α x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) g (FreeMonoid.of.{u2} α x))) -> (Eq.{max (succ u2) (succ u1)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f g)
 Case conversion may be inaccurate. Consider using '#align free_monoid.hom_eq FreeMonoid.hom_eqₓ'. -/
 @[ext, to_additive]
 theorem hom_eq ⦃f g : FreeMonoid α →* M⦄ (h : ∀ x, f (of x) = g (of x)) : f = g :=
@@ -370,7 +370,7 @@ def lift : (α → M) ≃ (FreeMonoid α →* M)
 lean 3 declaration is
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 but is expected to have type
-  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) f) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) 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(CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (α -> M)) (Equiv.symm.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.lift.{u2, u1} α M _inst_1)) f) (Function.comp.{succ u2, succ u2, succ u1} α (FreeMonoid.{u2} α) M (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f) (FreeMonoid.of.{u2} α))
+  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) f) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) 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(CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) => α -> M) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (α -> M)) (Equiv.symm.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.lift.{u2, u1} α M _inst_1)) f) (Function.comp.{succ u2, succ u2, succ u1} α (FreeMonoid.{u2} α) M (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) f) (FreeMonoid.of.{u2} α))
 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_symm_apply FreeMonoid.lift_symm_applyₓ'. -/
 @[simp, to_additive]
 theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of :=
@@ -382,7 +382,7 @@ theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_apply FreeMonoid.lift_applyₓ'. -/
 @[to_additive]
 theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = (l.toList.map f).Prod :=
@@ -394,7 +394,7 @@ theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = (l.toList.map
 lean 3 declaration is
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 but is expected to have type
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+  forall {α : Type.{u2}} {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] (f : α -> M), Eq.{max (succ u2) (succ u1)} (α -> M) (Function.comp.{succ u2, succ u2, succ u1} α (FreeMonoid.{u2} α) M (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => M) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) M (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) f) (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (Equiv.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1))) (α -> M) (fun (_x : α -> M) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α -> M) => MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1)) _x) (Equiv.instFunLikeEquiv.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (α -> M) (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) M (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} M _inst_1))) (FreeMonoid.lift.{u2, u1} α M _inst_1) f)) (FreeMonoid.of.{u2} α)) f
 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_comp_of FreeMonoid.lift_comp_ofₓ'. -/
 @[to_additive]
 theorem lift_comp_of (f : α → M) : lift f ∘ of = f :=
@@ -406,7 +406,7 @@ theorem lift_comp_of (f : α → M) : lift f ∘ of = f :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_eval_of FreeMonoid.lift_eval_ofₓ'. -/
 @[simp, to_additive]
 theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x :=
@@ -418,7 +418,7 @@ theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.lift_restrict FreeMonoid.lift_restrictₓ'. -/
 @[simp, to_additive]
 theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f :=
@@ -430,7 +430,7 @@ theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f :=
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align free_monoid.comp_lift FreeMonoid.comp_liftₓ'. -/
 @[to_additive]
 theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) :=
@@ -444,7 +444,7 @@ theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘
 lean 3 declaration is
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(FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)) (Function.comp.{succ u1, succ u3, succ u2} α M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)))) g) f)) (FreeMonoid.{u1} α) N (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α))))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α -> N) => MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)) (Function.comp.{succ u1, succ u3, succ u2} α M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) a) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)))) g) f)) (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), max (succ u2) (succ u1)} (Equiv.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (α -> N) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2))) (α -> N) (fun (_x : α -> N) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α -> N) => MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2)) _x) (Equiv.instFunLikeEquiv.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (α -> N) (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) N (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} N _inst_2))) (FreeMonoid.lift.{u1, u2} α N _inst_2) (Function.comp.{succ u1, succ u3, succ u2} α M N (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : M) => N) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N _inst_2)) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)) M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2) (MonoidHom.monoidHomClass.{u3, u2} M N (Monoid.toMulOneClass.{u3} M _inst_1) (Monoid.toMulOneClass.{u2} N _inst_2)))) g) f)) x)
 Case conversion may be inaccurate. Consider using '#align free_monoid.hom_map_lift FreeMonoid.hom_map_liftₓ'. -/
 @[to_additive]
 theorem hom_map_lift (g : M →* N) (f : α → M) (x : FreeMonoid α) : g (lift f x) = lift (g ∘ f) x :=
@@ -529,7 +529,7 @@ def map (f : α → β) : FreeMonoid α →* FreeMonoid β
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (x : α), Eq.{succ u2} (FreeMonoid.{u2} β) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) => (FreeMonoid.{u1} α) -> (FreeMonoid.{u2} β)) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) (FreeMonoid.map.{u1, u2} α β f) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u2} β (f x))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) (FreeMonoid.of.{u1} α x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (fun (_x : FreeMonoid.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α))))) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))))) (FreeMonoid.map.{u1, u2} α β f) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u2} β (f x))
+  forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (x : α), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) (FreeMonoid.of.{u1} α x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (fun (_x : FreeMonoid.{u1} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u1} α) => FreeMonoid.{u2} β) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α))))) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))) (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β)))) (MonoidHom.monoidHomClass.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} β))))))) (FreeMonoid.map.{u1, u2} α β f) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u2} β (f x))
 Case conversion may be inaccurate. Consider using '#align free_monoid.map_of FreeMonoid.map_ofₓ'. -/
 @[simp, to_additive]
 theorem map_of (f : α → β) (x : α) : map f (of x) = of (f x) :=
@@ -541,7 +541,7 @@ theorem map_of (f : α → β) (x : α) : map f (of x) = of (f x) :=
 lean 3 declaration is
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 but is expected to have type
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(FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))))) (FreeMonoid.map.{u2, u1} α β f) xs)) (List.map.{u2, u1} α β f (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : FreeMonoid.{u2} α) => List.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (FreeMonoid.{u2} α) (List.{u2} α)) (FreeMonoid.toList.{u2} α) xs))
 Case conversion may be inaccurate. Consider using '#align free_monoid.to_list_map FreeMonoid.toList_mapₓ'. -/
 @[to_additive]
 theorem toList_map (f : α → β) (xs : FreeMonoid α) : (map f xs).toList = xs.toList.map f :=
@@ -553,7 +553,7 @@ theorem toList_map (f : α → β) (xs : FreeMonoid α) : (map f xs).toList = xs
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} (f : α -> β) (xs : List.{u1} α), Eq.{succ u2} (FreeMonoid.{u2} β) (coeFn.{succ u2, succ u2} (Equiv.{succ u2, succ u2} (List.{u2} β) (FreeMonoid.{u2} β)) (fun (_x : Equiv.{succ u2, succ u2} (List.{u2} β) (FreeMonoid.{u2} β)) => (List.{u2} β) -> (FreeMonoid.{u2} β)) (Equiv.hasCoeToFun.{succ u2, succ u2} (List.{u2} β) (FreeMonoid.{u2} β)) (FreeMonoid.ofList.{u2} β) (List.map.{u1, u2} α β f xs)) (coeFn.{max (succ u2) (succ u1), max (succ u1) (succ u2)} (MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) (fun (_x : MonoidHom.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) => (FreeMonoid.{u1} α) -> (FreeMonoid.{u2} β)) (MonoidHom.hasCoeToFun.{u1, u2} (FreeMonoid.{u1} α) (FreeMonoid.{u2} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} β) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} β) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} β) (FreeMonoid.cancelMonoid.{u2} β))))) (FreeMonoid.map.{u1, u2} α β f) (coeFn.{succ u1, succ u1} (Equiv.{succ u1, succ u1} (List.{u1} α) (FreeMonoid.{u1} α)) (fun (_x : Equiv.{succ u1, succ u1} (List.{u1} α) (FreeMonoid.{u1} α)) => (List.{u1} α) -> (FreeMonoid.{u1} α)) (Equiv.hasCoeToFun.{succ u1, succ u1} (List.{u1} α) (FreeMonoid.{u1} α)) (FreeMonoid.ofList.{u1} α) xs))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (xs : List.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u1} β) => FreeMonoid.{u1} β) (List.map.{u2, u1} α β f xs)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (List.{u1} β) (FreeMonoid.{u1} β)) (List.{u1} β) (fun (_x : List.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u1} β) => FreeMonoid.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (List.{u1} β) (FreeMonoid.{u1} β)) (FreeMonoid.ofList.{u1} β) (List.map.{u2, u1} α β f xs)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : FreeMonoid.{u2} α) => FreeMonoid.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))))) (FreeMonoid.map.{u2, u1} α β f) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (List.{u2} α) (fun (_x : List.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u2} α) => FreeMonoid.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (FreeMonoid.ofList.{u2} α) xs))
+  forall {α : Type.{u2}} {β : Type.{u1}} (f : α -> β) (xs : List.{u2} α), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u1} β) => FreeMonoid.{u1} β) (List.map.{u2, u1} α β f xs)) (FunLike.coe.{succ u1, succ u1, succ u1} (Equiv.{succ u1, succ u1} (List.{u1} β) (FreeMonoid.{u1} β)) (List.{u1} β) (fun (_x : List.{u1} β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u1} β) => FreeMonoid.{u1} β) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u1} (List.{u1} β) (FreeMonoid.{u1} β)) (FreeMonoid.ofList.{u1} β) (List.map.{u2, u1} α β f xs)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (fun (_x : FreeMonoid.{u2} α) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : FreeMonoid.{u2} α) => FreeMonoid.{u1} β) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (MulOneClass.toMul.{u2} (FreeMonoid.{u2} α) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α))))) (MulOneClass.toMul.{u1} (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, u1} (MonoidHom.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))) (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β)))) (MonoidHom.monoidHomClass.{u2, u1} (FreeMonoid.{u2} α) (FreeMonoid.{u1} β) (Monoid.toMulOneClass.{u2} (FreeMonoid.{u2} α) (RightCancelMonoid.toMonoid.{u2} (FreeMonoid.{u2} α) (CancelMonoid.toRightCancelMonoid.{u2} (FreeMonoid.{u2} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u2} α)))) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} β) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} β) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} β) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} β))))))) (FreeMonoid.map.{u2, u1} α β f) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (List.{u2} α) (fun (_x : List.{u2} α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : List.{u2} α) => FreeMonoid.{u2} α) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (List.{u2} α) (FreeMonoid.{u2} α)) (FreeMonoid.ofList.{u2} α) xs))
 Case conversion may be inaccurate. Consider using '#align free_monoid.of_list_map FreeMonoid.ofList_mapₓ'. -/
 @[to_additive]
 theorem ofList_map (f : α → β) (xs : List α) : ofList (xs.map f) = map f (ofList xs) :=

657df433

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

657df433

chore(Algebra/BigOperators/List): Use Std lemmas (#11725)

Make Algebra.BigOperators.List.Basic, Data.List.Chain not depend on Data.Nat.Order.Basic by using Nat-specific Std lemmas rather than general mathlib ones. I leave the Data.Nat.Basic import since Algebra.BigOperators.List.Basic is algebra territory.
Make Algebra.BigOperators.List.Basic not depend on Algebra.Divisibility.Basic. I'm not too sure about that one since they already are algebra. My motivation is that they involve ring-like objects while big operators are about group-like objects, but this is in some sense a second order refactor.
As a consequence, move the divisibility and MonoidWithZero lemmas from Algebra.BigOperators.List.Basic to Algebra.BigOperators.List.Lemmas.
Move the content of Algebra.BigOperators.List.Defs to Algebra.BigOperators.List.Basic since no file imported the former without the latter and their imports are becoming very close after this PR.
Make Data.List.Count, Data.List.Dedup, Data.List.ProdSigma, Data.List.Zip not depend on Algebra.BigOperators.List.Basic.
As a consequence, move the big operators lemmas that were in there to Algebra.BigOperators.List.Basic. For the lemmas that were Nat -specific, keep a version of them stated using Nat.sum.
To help with this, add Nat.sum_eq_listSum (l : List Nat) : Nat.sum l = l.sum.

f7519d5e

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon, Yury Kudryashov
 -/
 import Mathlib.Algebra.BigOperators.List.Basic
+import Mathlib.Algebra.Group.Units
 import Mathlib.GroupTheory.GroupAction.Defs
 
 #align_import algebra.free_monoid.basic from "leanprover-community/mathlib"@"657df4339ae6ceada048c8a2980fb10e393143ec"

657df433

move(Data/List/BigOperators): Move to Algebra.BigOperators.List (#11729)

This is algebra and should be foldered as such.

f09ccf67

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Simon Hudon. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon, Yury Kudryashov
 -/
-import Mathlib.Data.List.BigOperators.Basic
+import Mathlib.Algebra.BigOperators.List.Basic
 import Mathlib.GroupTheory.GroupAction.Defs
 
 #align_import algebra.free_monoid.basic from "leanprover-community/mathlib"@"657df4339ae6ceada048c8a2980fb10e393143ec"

657df433

chore: classify new theorem / theorem porting notes (#11432)

Classifies by adding issue number #10756 to porting notes claiming anything equivalent to:

"added theorem"
"added theorems"
"new theorem"
"new theorems"
"added lemma"
"new lemma"
"new lemmas"

55fe4027

Diff

@@ -231,7 +231,7 @@ def lift : (α → M) ≃ (FreeMonoid α →* M) where
 #align free_monoid.lift FreeMonoid.lift
 #align free_add_monoid.lift FreeAddMonoid.lift
 
--- Porting note: new
+-- Porting note (#10756): new theorem
 @[to_additive (attr := simp)]
 theorem lift_ofList (f : α → M) (l : List α) : lift f (ofList l) = (l.map f).prod :=
   prodAux_eq _

657df433

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -231,7 +231,7 @@ def lift : (α → M) ≃ (FreeMonoid α →* M) where
 #align free_monoid.lift FreeMonoid.lift
 #align free_add_monoid.lift FreeAddMonoid.lift
 
--- porting note: new
+-- Porting note: new
 @[to_additive (attr := simp)]
 theorem lift_ofList (f : α → M) (l : List α) : lift f (ofList l) = (l.map f).prod :=
   prodAux_eq _

657df433

chore: remove duplicates about List.append (#9376)

Replace duplicates in Mathlib with theorems in Lean core.

List.append_left_cancel → List.append_cancel_left
List.append_right_cancel → List.append_cancel_right

8fb1d5ae

Diff

@@ -81,8 +81,8 @@ instance : CancelMonoid (FreeMonoid α)
   mul_one := List.append_nil
   one_mul := List.nil_append
   mul_assoc := List.append_assoc
-  mul_left_cancel _ _ _ := List.append_left_cancel
-  mul_right_cancel _ _ _ := List.append_right_cancel
+  mul_left_cancel _ _ _ := List.append_cancel_left
+  mul_right_cancel _ _ _ := List.append_cancel_right
 
 @[to_additive]
 instance : Inhabited (FreeMonoid α) := ⟨1⟩

657df433

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

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

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

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

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

82656743

Diff

@@ -271,7 +271,7 @@ theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘
 
 @[to_additive]
 theorem hom_map_lift (g : M →* N) (f : α → M) (x : FreeMonoid α) : g (lift f x) = lift (g ∘ f) x :=
-  FunLike.ext_iff.1 (comp_lift g f) x
+  DFunLike.ext_iff.1 (comp_lift g f) x
 #align free_monoid.hom_map_lift FreeMonoid.hom_map_lift
 #align free_add_monoid.hom_map_lift FreeAddMonoid.hom_map_lift
 
@@ -351,7 +351,7 @@ theorem map_id : map (@id α) = MonoidHom.id (FreeMonoid α) := hom_eq fun _ ↦
 @[to_additive]
 instance uniqueUnits : Unique (FreeMonoid α)ˣ where
   uniq u := Units.ext <| toList.injective <|
-    have : toList u.val ++ toList u.inv = [] := FunLike.congr_arg toList u.val_inv
+    have : toList u.val ++ toList u.inv = [] := DFunLike.congr_arg toList u.val_inv
     (List.append_eq_nil.mp this).1
 
 end FreeMonoid

657df433

chore: delete DecidableEq instance in Algebra.FreeMonoid.Basic (#9741)

9cf9e375

Diff

@@ -31,10 +31,6 @@ def FreeMonoid (α) := List α
 
 namespace FreeMonoid
 
--- Porting note: TODO. Check this is still needed
-@[to_additive]
-instance [DecidableEq α] : DecidableEq (FreeMonoid α) := instDecidableEqList
-
 /-- The identity equivalence between `FreeMonoid α` and `List α`. -/
 @[to_additive "The identity equivalence between `FreeAddMonoid α` and `List α`."]
 def toList : FreeMonoid α ≃ List α := Equiv.refl _

657df433

chore: Generalise monotonicity of multiplication lemmas to semirings (#9369)

Many lemmas about BlahOrderedRing α did not mention negation. I could generalise almost all those lemmas to BlahOrderedSemiring α + ExistsAddOfLE α except for a series of five lemmas (left a TODO about them).

Now those lemmas apply to things like the naturals. This is not very useful on its own, because those lemmas are trivially true on canonically ordered semirings (they are about multiplication by negative elements, of which there are none, or nonnegativity of squares, but we already know everything is nonnegative), except that I will soon add more complicated inequalities that are based on those, and it would be a shame having to write two versions of each: one for ordered rings, one for canonically ordered semirings.

A similar refactor could be made for scalar multiplication, but this PR is big enough already.

From LeanAPAP

0c9d4118

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon, Yury Kudryashov
 -/
 import Mathlib.Data.List.BigOperators.Basic
+import Mathlib.GroupTheory.GroupAction.Defs
 
 #align_import algebra.free_monoid.basic from "leanprover-community/mathlib"@"657df4339ae6ceada048c8a2980fb10e393143ec"

657df433

feat(Algebra/FreeMonoid): the units are unique (#8904)

886b5aa7

Diff

@@ -350,4 +350,11 @@ theorem map_id : map (@id α) = MonoidHom.id (FreeMonoid α) := hom_eq fun _ ↦
 #align free_monoid.map_id FreeMonoid.map_id
 #align free_add_monoid.map_id FreeAddMonoid.map_id
 
+/-- The only invertible element of the free monoid is 1; this instance enables `units_eq_one`. -/
+@[to_additive]
+instance uniqueUnits : Unique (FreeMonoid α)ˣ where
+  uniq u := Units.ext <| toList.injective <|
+    have : toList u.val ++ toList u.inv = [] := FunLike.congr_arg toList u.val_inv
+    (List.append_eq_nil.mp this).1
+
 end FreeMonoid

657df433

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -20,7 +20,7 @@ import Mathlib.Data.List.BigOperators.Basic
 -/
 
 
-variable {α : Type _} {β : Type _} {γ : Type _} {M : Type _} [Monoid M] {N : Type _} [Monoid N]
+variable {α : Type*} {β : Type*} {γ : Type*} {M : Type*} [Monoid M] {N : Type*} [Monoid N]
 
 /-- Free monoid over a given alphabet. -/
 @[to_additive "Free nonabelian additive monoid over a given alphabet"]
@@ -157,19 +157,19 @@ theorem of_injective : Function.Injective (@of α) := List.singleton_injective
 @[to_additive (attr := elab_as_elim) "Recursor for `FreeAddMonoid` using `0` and
 `FreeAddMonoid.of x + xs` instead of `[]` and `x :: xs`."]
 -- Porting note: change from `List.recOn` to `List.rec` since only the latter is computable
-def recOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
+def recOn {C : FreeMonoid α → Sort*} (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C xs → C (of x * xs)) : C xs := List.rec h0 ih xs
 #align free_monoid.rec_on FreeMonoid.recOn
 #align free_add_monoid.rec_on FreeAddMonoid.recOn
 
 @[to_additive (attr := simp)]
-theorem recOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C xs → C (of x * xs)) :
+theorem recOn_one {C : FreeMonoid α → Sort*} (h0 : C 1) (ih : ∀ x xs, C xs → C (of x * xs)) :
     @recOn α C 1 h0 ih = h0 := rfl
 #align free_monoid.rec_on_one FreeMonoid.recOn_one
 #align free_add_monoid.rec_on_zero FreeAddMonoid.recOn_zero
 
 @[to_additive (attr := simp)]
-theorem recOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α) (h0 : C 1)
+theorem recOn_of_mul {C : FreeMonoid α → Sort*} (x : α) (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C xs → C (of x * xs)) : @recOn α C (of x * xs) h0 ih = ih x xs (recOn xs h0 ih) :=
   rfl
 #align free_monoid.rec_on_of_mul FreeMonoid.recOn_of_mul
@@ -179,19 +179,19 @@ theorem recOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α
 `[]` and `x :: xs`. -/
 @[to_additive (attr := elab_as_elim) "A version of `List.casesOn` for `FreeAddMonoid` using `0` and
 `FreeAddMonoid.of x + xs` instead of `[]` and `x :: xs`."]
-def casesOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
+def casesOn {C : FreeMonoid α → Sort*} (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C (of x * xs)) : C xs := List.casesOn xs h0 ih
 #align free_monoid.cases_on FreeMonoid.casesOn
 #align free_add_monoid.cases_on FreeAddMonoid.casesOn
 
 @[to_additive (attr := simp)]
-theorem casesOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C (of x * xs)) :
+theorem casesOn_one {C : FreeMonoid α → Sort*} (h0 : C 1) (ih : ∀ x xs, C (of x * xs)) :
     @casesOn α C 1 h0 ih = h0 := rfl
 #align free_monoid.cases_on_one FreeMonoid.casesOn_one
 #align free_add_monoid.cases_on_zero FreeAddMonoid.casesOn_zero
 
 @[to_additive (attr := simp)]
-theorem casesOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α) (h0 : C 1)
+theorem casesOn_of_mul {C : FreeMonoid α → Sort*} (x : α) (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C (of x * xs)) : @casesOn α C (of x * xs) h0 ih = ih x xs := rfl
 #align free_monoid.cases_on_of_mul FreeMonoid.casesOn_of_mul
 #align free_add_monoid.cases_on_of_add FreeAddMonoid.casesOn_of_add

657df433

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2019 Simon Hudon. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon, Yury Kudryashov
-
-! This file was ported from Lean 3 source module algebra.free_monoid.basic
-! leanprover-community/mathlib commit 657df4339ae6ceada048c8a2980fb10e393143ec
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.List.BigOperators.Basic
 
+#align_import algebra.free_monoid.basic from "leanprover-community/mathlib"@"657df4339ae6ceada048c8a2980fb10e393143ec"
+
 /-!
 # Free monoid over a given alphabet

657df433

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

12343aa5

Diff

@@ -202,7 +202,7 @@ theorem casesOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid
 @[to_additive (attr := ext)]
 theorem hom_eq ⦃f g : FreeMonoid α →* M⦄ (h : ∀ x, f (of x) = g (of x)) : f = g :=
   MonoidHom.ext fun l ↦ recOn l (f.map_one.trans g.map_one.symm)
-    (fun x xs hxs ↦ by  simp only [h, hxs, MonoidHom.map_mul])
+    (fun x xs hxs ↦ by simp only [h, hxs, MonoidHom.map_mul])
 #align free_monoid.hom_eq FreeMonoid.hom_eq
 #align free_add_monoid.hom_eq FreeAddMonoid.hom_eq
 
@@ -211,14 +211,14 @@ The purpose is to make `FreeMonoid.lift_eval_of` true by `rfl`. -/
 @[to_additive "A variant of `List.sum` that has `[x].sum = x` true definitionally.
 The purpose is to make `FreeAddMonoid.lift_eval_of` true by `rfl`."]
 def prodAux {M} [Monoid M] : List M → M
-  | []  => 1
+  | [] => 1
   | (x :: xs) => List.foldl (· * ·) x xs
 #align free_monoid.prod_aux FreeMonoid.prodAux
 #align free_add_monoid.sum_aux FreeAddMonoid.sumAux
 
 @[to_additive]
 lemma prodAux_eq : ∀ l : List M, FreeMonoid.prodAux l = l.prod
-  | []  => rfl
+  | [] => rfl
   | (_ :: xs) => congr_arg (fun x => List.foldl (· * ·) x xs) (one_mul _).symm
 #align free_monoid.prod_aux_eq FreeMonoid.prodAux_eq
 #align free_add_monoid.sum_aux_eq FreeAddMonoid.sumAux_eq

657df433

chore: cleanup of some ext porting notes (#5176)

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

6ffd1a5d

Diff

@@ -269,9 +269,9 @@ theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f := lift.a
 #align free_add_monoid.lift_restrict FreeAddMonoid.lift_restrict
 
 @[to_additive]
-theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) :=
-  -- Porting note: replace ext by FreeMonoid.hom_eq
-  FreeMonoid.hom_eq (by simp)
+theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) := by
+  ext
+  simp
 #align free_monoid.comp_lift FreeMonoid.comp_lift
 #align free_add_monoid.comp_lift FreeAddMonoid.comp_lift

657df433

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -240,7 +240,7 @@ def lift : (α → M) ≃ (FreeMonoid α →* M) where
 -- porting note: new
 @[to_additive (attr := simp)]
 theorem lift_ofList (f : α → M) (l : List α) : lift f (ofList l) = (l.map f).prod :=
-prodAux_eq _
+  prodAux_eq _
 
 @[to_additive (attr := simp)]
 theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of := rfl
@@ -249,7 +249,7 @@ theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of := r
 
 @[to_additive]
 theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = ((toList l).map f).prod :=
-prodAux_eq _
+  prodAux_eq _
 #align free_monoid.lift_apply FreeMonoid.lift_apply
 #align free_add_monoid.lift_apply FreeAddMonoid.lift_apply
 
@@ -270,7 +270,7 @@ theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f := lift.a
 
 @[to_additive]
 theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) :=
--- Porting note: replace ext by FreeMonoid.hom_eq
+  -- Porting note: replace ext by FreeMonoid.hom_eq
   FreeMonoid.hom_eq (by simp)
 #align free_monoid.comp_lift FreeMonoid.comp_lift
 #align free_add_monoid.comp_lift FreeAddMonoid.comp_lift

657df433

chore: update SHA from #1497 (#2050)

Comparing https://leanprover-community.github.io/mathlib-port-status/file/algebra/free_monoid/basic against #1497 shows that this is already up to date.

70ff72b4

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module algebra.free_monoid.basic
-! leanprover-community/mathlib commit dd71334db81d0bd444af1ee339a29298bef40734
+! leanprover-community/mathlib commit 657df4339ae6ceada048c8a2980fb10e393143ec
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

dd71334d

Fix: Move more attributes to the attr argument of to_additive (#2558)

e8072f65

Diff

@@ -180,7 +180,7 @@ theorem recOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α
 
 /-- A version of `List.cases_on` for `FreeMonoid` using `1` and `FreeMonoid.of x * xs` instead of
 `[]` and `x :: xs`. -/
-@[elab_as_elim, to_additive "A version of `List.casesOn` for `FreeAddMonoid` using `0` and
+@[to_additive (attr := elab_as_elim) "A version of `List.casesOn` for `FreeAddMonoid` using `0` and
 `FreeAddMonoid.of x + xs` instead of `[]` and `x :: xs`."]
 def casesOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C (of x * xs)) : C xs := List.casesOn xs h0 ih

dd71334d

feat: port LinearAlgebra.TensorProduct (#2539)

It was quite smooth. I didn't have to make changes that I expect to change downstream files, so I left few porting notes.

Comments that I didn't make into porting notes:

attribute [local ext] ext had to be changed to attribute [local ext high] ext
Sometimes M ⊗ N needed to be replaced by M ⊗[R] N in theorem statements.
I needed to make a few fixes in other files. I want to go through the library globally and fix this error, but I'm waiting on #1881 to get merged, because those two things would have many merge conflicts.

Co-authored-by: Johan Commelin <johan@commelin.net>

7b9199f9

Diff

@@ -157,8 +157,8 @@ theorem of_injective : Function.Injective (@of α) := List.singleton_injective
 #align free_add_monoid.of_injective FreeAddMonoid.of_injective
 
 /-- Recursor for `FreeMonoid` using `1` and `FreeMonoid.of x * xs` instead of `[]` and `x :: xs`. -/
-@[elab_as_elim, to_additive "Recursor for `FreeAddMonoid` using `0` and `FreeAddMonoid.of x + xs`
-instead of `[]` and `x :: xs`."]
+@[to_additive (attr := elab_as_elim) "Recursor for `FreeAddMonoid` using `0` and
+`FreeAddMonoid.of x + xs` instead of `[]` and `x :: xs`."]
 -- Porting note: change from `List.recOn` to `List.rec` since only the latter is computable
 def recOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C xs → C (of x * xs)) : C xs := List.rec h0 ih xs

dd71334d

feat: add FreeMonoid.lift_ofList (#2193)

f9619549

Diff

@@ -226,8 +226,7 @@ lemma prodAux_eq : ∀ l : List M, FreeMonoid.prodAux l = l.prod
 /-- Equivalence between maps `α → M` and monoid homomorphisms `FreeMonoid α →* M`. -/
 @[to_additive "Equivalence between maps `α → A` and additive monoid homomorphisms
 `FreeAddMonoid α →+ A`."]
-def lift : (α → M) ≃ (FreeMonoid α →* M)
-    where
+def lift : (α → M) ≃ (FreeMonoid α →* M) where
   toFun f :=
   { toFun := fun l ↦ prodAux ((toList l).map f)
     map_one' := rfl
@@ -238,6 +237,11 @@ def lift : (α → M) ≃ (FreeMonoid α →* M)
 #align free_monoid.lift FreeMonoid.lift
 #align free_add_monoid.lift FreeAddMonoid.lift
 
+-- porting note: new
+@[to_additive (attr := simp)]
+theorem lift_ofList (f : α → M) (l : List α) : lift f (ofList l) = (l.map f).prod :=
+prodAux_eq _
+
 @[to_additive (attr := simp)]
 theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of := rfl
 #align free_monoid.lift_symm_apply FreeMonoid.lift_symm_apply

dd71334d

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -213,11 +213,15 @@ The purpose is to make `FreeAddMonoid.lift_eval_of` true by `rfl`."]
 def prodAux {M} [Monoid M] : List M → M
   | []  => 1
   | (x :: xs) => List.foldl (· * ·) x xs
+#align free_monoid.prod_aux FreeMonoid.prodAux
+#align free_add_monoid.sum_aux FreeAddMonoid.sumAux
 
 @[to_additive]
 lemma prodAux_eq : ∀ l : List M, FreeMonoid.prodAux l = l.prod
   | []  => rfl
   | (_ :: xs) => congr_arg (fun x => List.foldl (· * ·) x xs) (one_mul _).symm
+#align free_monoid.prod_aux_eq FreeMonoid.prodAux_eq
+#align free_add_monoid.sum_aux_eq FreeAddMonoid.sumAux_eq
 
 /-- Equivalence between maps `α → M` and monoid homomorphisms `FreeMonoid α →* M`. -/
 @[to_additive "Equivalence between maps `α → A` and additive monoid homomorphisms

dd71334d

chore: add #align statements for to_additive decls (#1816)

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

ed378238

Diff

@@ -29,6 +29,7 @@ variable {α : Type _} {β : Type _} {γ : Type _} {M : Type _} [Monoid M] {N :
 @[to_additive "Free nonabelian additive monoid over a given alphabet"]
 def FreeMonoid (α) := List α
 #align free_monoid FreeMonoid
+#align free_add_monoid FreeAddMonoid
 
 namespace FreeMonoid
 
@@ -40,35 +41,43 @@ instance [DecidableEq α] : DecidableEq (FreeMonoid α) := instDecidableEqList
 @[to_additive "The identity equivalence between `FreeAddMonoid α` and `List α`."]
 def toList : FreeMonoid α ≃ List α := Equiv.refl _
 #align free_monoid.to_list FreeMonoid.toList
+#align free_add_monoid.to_list FreeAddMonoid.toList
 
 /-- The identity equivalence between `List α` and `FreeMonoid α`. -/
 @[to_additive "The identity equivalence between `List α` and `FreeAddMonoid α`."]
 def ofList : List α ≃ FreeMonoid α := Equiv.refl _
 #align free_monoid.of_list FreeMonoid.ofList
+#align free_add_monoid.of_list FreeAddMonoid.ofList
 
 @[to_additive (attr := simp)]
 theorem toList_symm : (@toList α).symm = ofList := rfl
 #align free_monoid.to_list_symm FreeMonoid.toList_symm
+#align free_add_monoid.to_list_symm FreeAddMonoid.toList_symm
 
 @[to_additive (attr := simp)]
 theorem ofList_symm : (@ofList α).symm = toList := rfl
 #align free_monoid.of_list_symm FreeMonoid.ofList_symm
+#align free_add_monoid.of_list_symm FreeAddMonoid.ofList_symm
 
 @[to_additive (attr := simp)]
 theorem toList_ofList (l : List α) : toList (ofList l) = l := rfl
 #align free_monoid.to_list_of_list FreeMonoid.toList_ofList
+#align free_add_monoid.to_list_of_list FreeAddMonoid.toList_ofList
 
 @[to_additive (attr := simp)]
 theorem ofList_toList (xs : FreeMonoid α) : ofList (toList xs) = xs := rfl
 #align free_monoid.of_list_to_list FreeMonoid.ofList_toList
+#align free_add_monoid.of_list_to_list FreeAddMonoid.ofList_toList
 
 @[to_additive (attr := simp)]
 theorem toList_comp_ofList : @toList α ∘ ofList = id := rfl
 #align free_monoid.to_list_comp_of_list FreeMonoid.toList_comp_ofList
+#align free_add_monoid.to_list_comp_of_list FreeAddMonoid.toList_comp_ofList
 
 @[to_additive (attr := simp)]
 theorem ofList_comp_toList : @ofList α ∘ toList = id := rfl
 #align free_monoid.of_list_comp_to_list FreeMonoid.ofList_comp_toList
+#align free_add_monoid.of_list_comp_to_list FreeAddMonoid.ofList_comp_toList
 
 @[to_additive]
 instance : CancelMonoid (FreeMonoid α)
@@ -87,53 +96,65 @@ instance : Inhabited (FreeMonoid α) := ⟨1⟩
 @[to_additive (attr := simp)]
 theorem toList_one : toList (1 : FreeMonoid α) = [] := rfl
 #align free_monoid.to_list_one FreeMonoid.toList_one
+#align free_add_monoid.to_list_zero FreeAddMonoid.toList_zero
 
 @[to_additive (attr := simp)]
 theorem ofList_nil : ofList ([] : List α) = 1 := rfl
 #align free_monoid.of_list_nil FreeMonoid.ofList_nil
+#align free_add_monoid.of_list_nil FreeAddMonoid.ofList_nil
 
 @[to_additive (attr := simp)]
 theorem toList_mul (xs ys : FreeMonoid α) : toList (xs * ys) = toList xs ++ toList ys := rfl
 #align free_monoid.to_list_mul FreeMonoid.toList_mul
+#align free_add_monoid.to_list_add FreeAddMonoid.toList_add
 
 @[to_additive (attr := simp)]
 theorem ofList_append (xs ys : List α) : ofList (xs ++ ys) = ofList xs * ofList ys := rfl
 #align free_monoid.of_list_append FreeMonoid.ofList_append
+#align free_add_monoid.of_list_append FreeAddMonoid.ofList_append
 
 @[to_additive (attr := simp)]
 theorem toList_prod (xs : List (FreeMonoid α)) : toList xs.prod = (xs.map toList).join := by
   induction xs <;> simp [*, List.join]
 #align free_monoid.to_list_prod FreeMonoid.toList_prod
+#align free_add_monoid.to_list_sum FreeAddMonoid.toList_sum
 
 @[to_additive (attr := simp)]
 theorem ofList_join (xs : List (List α)) : ofList xs.join = (xs.map ofList).prod :=
   toList.injective <| by simp
 #align free_monoid.of_list_join FreeMonoid.ofList_join
+#align free_add_monoid.of_list_join FreeAddMonoid.ofList_join
 
 /-- Embeds an element of `α` into `FreeMonoid α` as a singleton list. -/
 @[to_additive "Embeds an element of `α` into `FreeAddMonoid α` as a singleton list."]
 def of (x : α) : FreeMonoid α := ofList [x]
 #align free_monoid.of FreeMonoid.of
+#align free_add_monoid.of FreeAddMonoid.of
 
 @[to_additive (attr := simp)]
 theorem toList_of (x : α) : toList (of x) = [x] := rfl
 #align free_monoid.to_list_of FreeMonoid.toList_of
+#align free_add_monoid.to_list_of FreeAddMonoid.toList_of
 
 @[to_additive]
 theorem ofList_singleton (x : α) : ofList [x] = of x := rfl
 #align free_monoid.of_list_singleton FreeMonoid.ofList_singleton
+#align free_add_monoid.of_list_singleton FreeAddMonoid.ofList_singleton
 
 @[to_additive (attr := simp)]
 theorem ofList_cons (x : α) (xs : List α) : ofList (x :: xs) = of x * ofList xs := rfl
 #align free_monoid.of_list_cons FreeMonoid.ofList_cons
+#align free_add_monoid.of_list_cons FreeAddMonoid.ofList_cons
 
 @[to_additive]
 theorem toList_of_mul (x : α) (xs : FreeMonoid α) : toList (of x * xs) = x :: toList xs := rfl
 #align free_monoid.to_list_of_mul FreeMonoid.toList_of_mul
+#align free_add_monoid.to_list_of_add FreeAddMonoid.toList_of_add
 
 @[to_additive]
 theorem of_injective : Function.Injective (@of α) := List.singleton_injective
 #align free_monoid.of_injective FreeMonoid.of_injective
+#align free_add_monoid.of_injective FreeAddMonoid.of_injective
 
 /-- Recursor for `FreeMonoid` using `1` and `FreeMonoid.of x * xs` instead of `[]` and `x :: xs`. -/
 @[elab_as_elim, to_additive "Recursor for `FreeAddMonoid` using `0` and `FreeAddMonoid.of x + xs`
@@ -142,17 +163,20 @@ instead of `[]` and `x :: xs`."]
 def recOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C xs → C (of x * xs)) : C xs := List.rec h0 ih xs
 #align free_monoid.rec_on FreeMonoid.recOn
+#align free_add_monoid.rec_on FreeAddMonoid.recOn
 
 @[to_additive (attr := simp)]
 theorem recOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C xs → C (of x * xs)) :
     @recOn α C 1 h0 ih = h0 := rfl
 #align free_monoid.rec_on_one FreeMonoid.recOn_one
+#align free_add_monoid.rec_on_zero FreeAddMonoid.recOn_zero
 
 @[to_additive (attr := simp)]
 theorem recOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C xs → C (of x * xs)) : @recOn α C (of x * xs) h0 ih = ih x xs (recOn xs h0 ih) :=
   rfl
 #align free_monoid.rec_on_of_mul FreeMonoid.recOn_of_mul
+#align free_add_monoid.rec_on_of_add FreeAddMonoid.recOn_of_add
 
 /-- A version of `List.cases_on` for `FreeMonoid` using `1` and `FreeMonoid.of x * xs` instead of
 `[]` and `x :: xs`. -/
@@ -161,22 +185,26 @@ theorem recOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α
 def casesOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C (of x * xs)) : C xs := List.casesOn xs h0 ih
 #align free_monoid.cases_on FreeMonoid.casesOn
+#align free_add_monoid.cases_on FreeAddMonoid.casesOn
 
 @[to_additive (attr := simp)]
 theorem casesOn_one {C : FreeMonoid α → Sort _} (h0 : C 1) (ih : ∀ x xs, C (of x * xs)) :
     @casesOn α C 1 h0 ih = h0 := rfl
 #align free_monoid.cases_on_one FreeMonoid.casesOn_one
+#align free_add_monoid.cases_on_zero FreeAddMonoid.casesOn_zero
 
 @[to_additive (attr := simp)]
 theorem casesOn_of_mul {C : FreeMonoid α → Sort _} (x : α) (xs : FreeMonoid α) (h0 : C 1)
     (ih : ∀ x xs, C (of x * xs)) : @casesOn α C (of x * xs) h0 ih = ih x xs := rfl
 #align free_monoid.cases_on_of_mul FreeMonoid.casesOn_of_mul
+#align free_add_monoid.cases_on_of_add FreeAddMonoid.casesOn_of_add
 
 @[to_additive (attr := ext)]
 theorem hom_eq ⦃f g : FreeMonoid α →* M⦄ (h : ∀ x, f (of x) = g (of x)) : f = g :=
   MonoidHom.ext fun l ↦ recOn l (f.map_one.trans g.map_one.symm)
     (fun x xs hxs ↦ by  simp only [h, hxs, MonoidHom.map_mul])
 #align free_monoid.hom_eq FreeMonoid.hom_eq
+#align free_add_monoid.hom_eq FreeAddMonoid.hom_eq
 
 /-- A variant of `List.prod` that has `[x].prod = x` true definitionally.
 The purpose is to make `FreeMonoid.lift_eval_of` true by `rfl`. -/
@@ -204,38 +232,46 @@ def lift : (α → M) ≃ (FreeMonoid α →* M)
   left_inv f := rfl
   right_inv f := hom_eq fun x ↦ rfl
 #align free_monoid.lift FreeMonoid.lift
+#align free_add_monoid.lift FreeAddMonoid.lift
 
 @[to_additive (attr := simp)]
 theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of := rfl
 #align free_monoid.lift_symm_apply FreeMonoid.lift_symm_apply
+#align free_add_monoid.lift_symm_apply FreeAddMonoid.lift_symm_apply
 
 @[to_additive]
 theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = ((toList l).map f).prod :=
 prodAux_eq _
 #align free_monoid.lift_apply FreeMonoid.lift_apply
+#align free_add_monoid.lift_apply FreeAddMonoid.lift_apply
 
 @[to_additive]
 theorem lift_comp_of (f : α → M) : lift f ∘ of = f := rfl
 #align free_monoid.lift_comp_of FreeMonoid.lift_comp_of
+#align free_add_monoid.lift_comp_of FreeAddMonoid.lift_comp_of
 
 @[to_additive (attr := simp)]
 theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x := rfl
 #align free_monoid.lift_eval_of FreeMonoid.lift_eval_of
+#align free_add_monoid.lift_eval_of FreeAddMonoid.lift_eval_of
 
 @[to_additive (attr := simp)]
 theorem lift_restrict (f : FreeMonoid α →* M) : lift (f ∘ of) = f := lift.apply_symm_apply f
 #align free_monoid.lift_restrict FreeMonoid.lift_restrict
+#align free_add_monoid.lift_restrict FreeAddMonoid.lift_restrict
 
 @[to_additive]
 theorem comp_lift (g : M →* N) (f : α → M) : g.comp (lift f) = lift (g ∘ f) :=
 -- Porting note: replace ext by FreeMonoid.hom_eq
   FreeMonoid.hom_eq (by simp)
 #align free_monoid.comp_lift FreeMonoid.comp_lift
+#align free_add_monoid.comp_lift FreeAddMonoid.comp_lift
 
 @[to_additive]
 theorem hom_map_lift (g : M →* N) (f : α → M) (x : FreeMonoid α) : g (lift f x) = lift (g ∘ f) x :=
   FunLike.ext_iff.1 (comp_lift g f) x
 #align free_monoid.hom_map_lift FreeMonoid.hom_map_lift
+#align free_add_monoid.hom_map_lift FreeAddMonoid.hom_map_lift
 
 /-- Define a multiplicative action of `FreeMonoid α` on `β`. -/
 @[to_additive "Define an additive action of `FreeAddMonoid α` on `β`."]
@@ -244,24 +280,28 @@ def mkMulAction (f : α → β → β) : MulAction (FreeMonoid α) β where
   one_smul _ := rfl
   mul_smul _ _ _ := List.foldr_append _ _ _ _
 #align free_monoid.mk_mul_action FreeMonoid.mkMulAction
+#align free_add_monoid.mk_add_action FreeAddMonoid.mkAddAction
 
 @[to_additive]
 theorem smul_def (f : α → β → β) (l : FreeMonoid α) (b : β) :
     haveI := mkMulAction f
     l • b = l.toList.foldr f b := rfl
 #align free_monoid.smul_def FreeMonoid.smul_def
+#align free_add_monoid.vadd_def FreeAddMonoid.vadd_def
 
 @[to_additive]
 theorem ofList_smul (f : α → β → β) (l : List α) (b : β) :
     haveI := mkMulAction f
     ofList l • b = l.foldr f b := rfl
 #align free_monoid.of_list_smul FreeMonoid.ofList_smul
+#align free_add_monoid.of_list_vadd FreeAddMonoid.ofList_vadd
 
 @[to_additive (attr := simp)]
 theorem of_smul (f : α → β → β) (x : α) (y : β) :
     (haveI := mkMulAction f
     of x • y) = f x y := rfl
 #align free_monoid.of_smul FreeMonoid.of_smul
+#align free_add_monoid.of_vadd FreeAddMonoid.of_vadd
 
 /-- The unique monoid homomorphism `FreeMonoid α →* FreeMonoid β` that sends
 each `of x` to `of (f x)`. -/
@@ -273,29 +313,36 @@ def map (f : α → β) : FreeMonoid α →* FreeMonoid β
   map_one' := rfl
   map_mul' _ _ := List.map_append _ _ _
 #align free_monoid.map FreeMonoid.map
+#align free_add_monoid.map FreeAddMonoid.map
 
 @[to_additive (attr := simp)]
 theorem map_of (f : α → β) (x : α) : map f (of x) = of (f x) := rfl
 #align free_monoid.map_of FreeMonoid.map_of
+#align free_add_monoid.map_of FreeAddMonoid.map_of
 
 @[to_additive]
 theorem toList_map (f : α → β) (xs : FreeMonoid α) : toList (map f xs) = xs.toList.map f := rfl
 #align free_monoid.to_list_map FreeMonoid.toList_map
+#align free_add_monoid.to_list_map FreeAddMonoid.toList_map
 
 @[to_additive]
 theorem ofList_map (f : α → β) (xs : List α) : ofList (xs.map f) = map f (ofList xs) := rfl
 #align free_monoid.of_list_map FreeMonoid.ofList_map
+#align free_add_monoid.of_list_map FreeAddMonoid.ofList_map
 
 @[to_additive]
 theorem lift_of_comp_eq_map (f : α → β) : (lift fun x ↦ of (f x)) = map f := hom_eq fun _ ↦ rfl
 #align free_monoid.lift_of_comp_eq_map FreeMonoid.lift_of_comp_eq_map
+#align free_add_monoid.lift_of_comp_eq_map FreeAddMonoid.lift_of_comp_eq_map
 
 @[to_additive]
 theorem map_comp (g : β → γ) (f : α → β) : map (g ∘ f) = (map g).comp (map f) := hom_eq fun _ ↦ rfl
 #align free_monoid.map_comp FreeMonoid.map_comp
+#align free_add_monoid.map_comp FreeAddMonoid.map_comp
 
 @[to_additive (attr := simp)]
 theorem map_id : map (@id α) = MonoidHom.id (FreeMonoid α) := hom_eq fun _ ↦ rfl
 #align free_monoid.map_id FreeMonoid.map_id
+#align free_add_monoid.map_id FreeAddMonoid.map_id
 
 end FreeMonoid

dd71334d

fix: make List.rec and Nat.rec computable (#1720)

This works around https://github.com/leanprover/lean4/issues/2049. By manually adding compiler support for these recursors, we make a large number of porting notes redundant.

19e2b8d2

Diff

@@ -138,9 +138,9 @@ theorem of_injective : Function.Injective (@of α) := List.singleton_injective
 /-- Recursor for `FreeMonoid` using `1` and `FreeMonoid.of x * xs` instead of `[]` and `x :: xs`. -/
 @[elab_as_elim, to_additive "Recursor for `FreeAddMonoid` using `0` and `FreeAddMonoid.of x + xs`
 instead of `[]` and `x :: xs`."]
--- Porting note: added noncomputable
-noncomputable def recOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
-    (ih : ∀ x xs, C xs → C (of x * xs)) : C xs := List.recOn xs h0 ih
+-- Porting note: change from `List.recOn` to `List.rec` since only the latter is computable
+def recOn {C : FreeMonoid α → Sort _} (xs : FreeMonoid α) (h0 : C 1)
+    (ih : ∀ x xs, C xs → C (of x * xs)) : C xs := List.rec h0 ih xs
 #align free_monoid.rec_on FreeMonoid.recOn
 
 @[to_additive (attr := simp)]

dd71334d

feat: forward port leanprover-community/mathlib#18121 (#1497)

91043fd8

Diff

@@ -178,18 +178,31 @@ theorem hom_eq ⦃f g : FreeMonoid α →* M⦄ (h : ∀ x, f (of x) = g (of x))
     (fun x xs hxs ↦ by  simp only [h, hxs, MonoidHom.map_mul])
 #align free_monoid.hom_eq FreeMonoid.hom_eq
 
+/-- A variant of `List.prod` that has `[x].prod = x` true definitionally.
+The purpose is to make `FreeMonoid.lift_eval_of` true by `rfl`. -/
+@[to_additive "A variant of `List.sum` that has `[x].sum = x` true definitionally.
+The purpose is to make `FreeAddMonoid.lift_eval_of` true by `rfl`."]
+def prodAux {M} [Monoid M] : List M → M
+  | []  => 1
+  | (x :: xs) => List.foldl (· * ·) x xs
+
+@[to_additive]
+lemma prodAux_eq : ∀ l : List M, FreeMonoid.prodAux l = l.prod
+  | []  => rfl
+  | (_ :: xs) => congr_arg (fun x => List.foldl (· * ·) x xs) (one_mul _).symm
+
 /-- Equivalence between maps `α → M` and monoid homomorphisms `FreeMonoid α →* M`. -/
 @[to_additive "Equivalence between maps `α → A` and additive monoid homomorphisms
 `FreeAddMonoid α →+ A`."]
 def lift : (α → M) ≃ (FreeMonoid α →* M)
     where
   toFun f :=
-  { toFun := fun l ↦ ((toList l).map f).prod
-    map_one' := rfl -- sorry
-    map_mul' := fun _ _ ↦ by simp only [toList_mul, List.map_append, List.prod_append] }
+  { toFun := fun l ↦ prodAux ((toList l).map f)
+    map_one' := rfl
+    map_mul' := fun _ _ ↦ by simp only [prodAux_eq, toList_mul, List.map_append, List.prod_append] }
   invFun f x := f (of x)
-  left_inv f := funext fun x ↦ one_mul (f x)
-  right_inv f := hom_eq fun x ↦ one_mul (f (of x))
+  left_inv f := rfl
+  right_inv f := hom_eq fun x ↦ rfl
 #align free_monoid.lift FreeMonoid.lift
 
 @[to_additive (attr := simp)]
@@ -197,15 +210,16 @@ theorem lift_symm_apply (f : FreeMonoid α →* M) : lift.symm f = f ∘ of := r
 #align free_monoid.lift_symm_apply FreeMonoid.lift_symm_apply
 
 @[to_additive]
-theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = ((toList l).map f).prod := rfl
+theorem lift_apply (f : α → M) (l : FreeMonoid α) : lift f l = ((toList l).map f).prod :=
+prodAux_eq _
 #align free_monoid.lift_apply FreeMonoid.lift_apply
 
 @[to_additive]
-theorem lift_comp_of (f : α → M) : lift f ∘ of = f := lift.symm_apply_apply f
+theorem lift_comp_of (f : α → M) : lift f ∘ of = f := rfl
 #align free_monoid.lift_comp_of FreeMonoid.lift_comp_of
 
 @[to_additive (attr := simp)]
-theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x := congr_fun (lift_comp_of f) x
+theorem lift_eval_of (f : α → M) (x : α) : lift f (of x) = f x := rfl
 #align free_monoid.lift_eval_of FreeMonoid.lift_eval_of
 
 @[to_additive (attr := simp)]

dd71334d

feat port:Algebra.FreeMonoid.Basic (#1443)

Dot notation not working for toList so replaced with "normal" notation

6420fef1

`algebra.free_monoid.basic` ⟷ `Mathlib.Algebra.FreeMonoid.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 2 + 87

algebra.free_monoid.basic ⟷ Mathlib.Algebra.FreeMonoid.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 2 + 87

`algebra.free_monoid.basic` ⟷ `Mathlib.Algebra.FreeMonoid.Basic`