group_theory.semidirect_product ⟷ Mathlib.GroupTheory.SemidirectProduct

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

@@ -3,7 +3,7 @@ Copyright (c) 2020 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Algebra.Hom.Aut
+import Algebra.Group.Aut
 import Logic.Function.Basic
 import GroupTheory.Subgroup.Basic
 

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

@@ -276,7 +276,7 @@ def lift (f₁ : N →* H) (f₂ : G →* H)
   map_one' := by simp
   map_mul' a b := by
     have := fun n g => MonoidHom.ext_iff.1 (h n) g
-    simp only [MulAut.conj_apply, MonoidHom.comp_apply, MulEquiv.coe_toMonoidHom] at this 
+    simp only [MulAut.conj_apply, MonoidHom.comp_apply, MulEquiv.coe_toMonoidHom] at this
     simp [this, mul_assoc]
 #align semidirect_product.lift SemidirectProduct.lift
 -/

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.Algebra.Hom.Aut
-import Mathbin.Logic.Function.Basic
-import Mathbin.GroupTheory.Subgroup.Basic
+import Algebra.Hom.Aut
+import Logic.Function.Basic
+import GroupTheory.Subgroup.Basic
 
 #align_import group_theory.semidirect_product from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"
 

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

@@ -65,7 +65,7 @@ instance : Group (N ⋊[φ] G) where
   mul_assoc a b c := by ext <;> simp [mul_assoc]
   one_mul a := ext _ _ (by simp) (one_mul a.2)
   mul_one a := ext _ _ (by simp) (mul_one _)
-  mul_left_inv := fun ⟨a, b⟩ => ext _ _ (show φ b⁻¹ a⁻¹ * φ b⁻¹ a = 1 by simp) (mul_left_inv b)
+  hMul_left_inv := fun ⟨a, b⟩ => ext _ _ (show φ b⁻¹ a⁻¹ * φ b⁻¹ a = 1 by simp) (mul_left_inv b)
 
 instance : Inhabited (N ⋊[φ] G) :=
   ⟨1⟩

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module group_theory.semidirect_product
-! leanprover-community/mathlib commit 68d1483e8a718ec63219f0e227ca3f0140361086
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Hom.Aut
 import Mathbin.Logic.Function.Basic
 import Mathbin.GroupTheory.Subgroup.Basic
 
+#align_import group_theory.semidirect_product from "leanprover-community/mathlib"@"68d1483e8a718ec63219f0e227ca3f0140361086"
+
 /-!
 # Semidirect product
 

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

@@ -41,6 +41,7 @@ group, semidirect product
 
 variable (N : Type _) (G : Type _) {H : Type _} [Group N] [Group G] [Group H]
 
+#print SemidirectProduct /-
 /-- The semidirect product of groups `N` and `G`, given a map `φ` from `G` to the automorphism
   group of `N`. It the product of sets with the group operation
   `⟨n₁, g₁⟩ * ⟨n₂, g₂⟩ = ⟨n₁ * φ g₁ n₂, g₁ * g₂⟩` -/
@@ -50,10 +51,10 @@ structure SemidirectProduct (φ : G →* MulAut N) where
   right : G
   deriving DecidableEq
 #align semidirect_product SemidirectProduct
+-/
 
 attribute [pp_using_anonymous_constructor] SemidirectProduct
 
--- mathport name: «expr ⋊[ ] »
 notation:35 N " ⋊[" φ:35 "] " G:35 => SemidirectProduct N G φ
 
 namespace SemidirectProduct
@@ -72,147 +73,204 @@ instance : Group (N ⋊[φ] G) where
 instance : Inhabited (N ⋊[φ] G) :=
   ⟨1⟩
 
+#print SemidirectProduct.one_left /-
 @[simp]
 theorem one_left : (1 : N ⋊[φ] G).left = 1 :=
   rfl
 #align semidirect_product.one_left SemidirectProduct.one_left
+-/
 
+#print SemidirectProduct.one_right /-
 @[simp]
 theorem one_right : (1 : N ⋊[φ] G).right = 1 :=
   rfl
 #align semidirect_product.one_right SemidirectProduct.one_right
+-/
 
+#print SemidirectProduct.inv_left /-
 @[simp]
 theorem inv_left (a : N ⋊[φ] G) : a⁻¹.left = φ a.right⁻¹ a.left⁻¹ :=
   rfl
 #align semidirect_product.inv_left SemidirectProduct.inv_left
+-/
 
+#print SemidirectProduct.inv_right /-
 @[simp]
 theorem inv_right (a : N ⋊[φ] G) : a⁻¹.right = a.right⁻¹ :=
   rfl
 #align semidirect_product.inv_right SemidirectProduct.inv_right
+-/
 
+#print SemidirectProduct.mul_left /-
 @[simp]
 theorem mul_left (a b : N ⋊[φ] G) : (a * b).left = a.left * φ a.right b.left :=
   rfl
 #align semidirect_product.mul_left SemidirectProduct.mul_left
+-/
 
+#print SemidirectProduct.mul_right /-
 @[simp]
 theorem mul_right (a b : N ⋊[φ] G) : (a * b).right = a.right * b.right :=
   rfl
 #align semidirect_product.mul_right SemidirectProduct.mul_right
+-/
 
+#print SemidirectProduct.inl /-
 /-- The canonical map `N →* N ⋊[φ] G` sending `n` to `⟨n, 1⟩` -/
 def inl : N →* N ⋊[φ] G where
   toFun n := ⟨n, 1⟩
   map_one' := rfl
   map_mul' := by intros <;> ext <;> simp
 #align semidirect_product.inl SemidirectProduct.inl
+-/
 
+#print SemidirectProduct.left_inl /-
 @[simp]
 theorem left_inl (n : N) : (inl n : N ⋊[φ] G).left = n :=
   rfl
 #align semidirect_product.left_inl SemidirectProduct.left_inl
+-/
 
+#print SemidirectProduct.right_inl /-
 @[simp]
 theorem right_inl (n : N) : (inl n : N ⋊[φ] G).right = 1 :=
   rfl
 #align semidirect_product.right_inl SemidirectProduct.right_inl
+-/
 
+#print SemidirectProduct.inl_injective /-
 theorem inl_injective : Function.Injective (inl : N → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨left, left_inl⟩
 #align semidirect_product.inl_injective SemidirectProduct.inl_injective
+-/
 
+#print SemidirectProduct.inl_inj /-
 @[simp]
 theorem inl_inj {n₁ n₂ : N} : (inl n₁ : N ⋊[φ] G) = inl n₂ ↔ n₁ = n₂ :=
   inl_injective.eq_iff
 #align semidirect_product.inl_inj SemidirectProduct.inl_inj
+-/
 
+#print SemidirectProduct.inr /-
 /-- The canonical map `G →* N ⋊[φ] G` sending `g` to `⟨1, g⟩` -/
 def inr : G →* N ⋊[φ] G where
   toFun g := ⟨1, g⟩
   map_one' := rfl
   map_mul' := by intros <;> ext <;> simp
 #align semidirect_product.inr SemidirectProduct.inr
+-/
 
+#print SemidirectProduct.left_inr /-
 @[simp]
 theorem left_inr (g : G) : (inr g : N ⋊[φ] G).left = 1 :=
   rfl
 #align semidirect_product.left_inr SemidirectProduct.left_inr
+-/
 
+#print SemidirectProduct.right_inr /-
 @[simp]
 theorem right_inr (g : G) : (inr g : N ⋊[φ] G).right = g :=
   rfl
 #align semidirect_product.right_inr SemidirectProduct.right_inr
+-/
 
+#print SemidirectProduct.inr_injective /-
 theorem inr_injective : Function.Injective (inr : G → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨right, right_inr⟩
 #align semidirect_product.inr_injective SemidirectProduct.inr_injective
+-/
 
+#print SemidirectProduct.inr_inj /-
 @[simp]
 theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ = g₂ :=
   inr_injective.eq_iff
 #align semidirect_product.inr_inj SemidirectProduct.inr_inj
+-/
 
+#print SemidirectProduct.inl_aut /-
 theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n * inr g⁻¹ := by
   ext <;> simp
 #align semidirect_product.inl_aut SemidirectProduct.inl_aut
+-/
 
+#print SemidirectProduct.inl_aut_inv /-
 theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr g⁻¹ * inl n * inr g := by
   rw [← MonoidHom.map_inv, inl_aut, inv_inv]
 #align semidirect_product.inl_aut_inv SemidirectProduct.inl_aut_inv
+-/
 
+#print SemidirectProduct.mk_eq_inl_mul_inr /-
 @[simp]
 theorem mk_eq_inl_mul_inr (g : G) (n : N) : (⟨n, g⟩ : N ⋊[φ] G) = inl n * inr g := by ext <;> simp
 #align semidirect_product.mk_eq_inl_mul_inr SemidirectProduct.mk_eq_inl_mul_inr
+-/
 
+#print SemidirectProduct.inl_left_mul_inr_right /-
 @[simp]
 theorem inl_left_mul_inr_right (x : N ⋊[φ] G) : inl x.left * inr x.right = x := by ext <;> simp
 #align semidirect_product.inl_left_mul_inr_right SemidirectProduct.inl_left_mul_inr_right
+-/
 
+#print SemidirectProduct.rightHom /-
 /-- The canonical projection map `N ⋊[φ] G →* G`, as a group hom. -/
 def rightHom : N ⋊[φ] G →* G where
   toFun := SemidirectProduct.right
   map_one' := rfl
   map_mul' _ _ := rfl
 #align semidirect_product.right_hom SemidirectProduct.rightHom
+-/
 
+#print SemidirectProduct.rightHom_eq_right /-
 @[simp]
 theorem rightHom_eq_right : (rightHom : N ⋊[φ] G → G) = right :=
   rfl
 #align semidirect_product.right_hom_eq_right SemidirectProduct.rightHom_eq_right
+-/
 
+#print SemidirectProduct.rightHom_comp_inl /-
 @[simp]
 theorem rightHom_comp_inl : (rightHom : N ⋊[φ] G →* G).comp inl = 1 := by ext <;> simp [right_hom]
 #align semidirect_product.right_hom_comp_inl SemidirectProduct.rightHom_comp_inl
+-/
 
+#print SemidirectProduct.rightHom_comp_inr /-
 @[simp]
 theorem rightHom_comp_inr : (rightHom : N ⋊[φ] G →* G).comp inr = MonoidHom.id _ := by
   ext <;> simp [right_hom]
 #align semidirect_product.right_hom_comp_inr SemidirectProduct.rightHom_comp_inr
+-/
 
+#print SemidirectProduct.rightHom_inl /-
 @[simp]
 theorem rightHom_inl (n : N) : rightHom (inl n : N ⋊[φ] G) = 1 := by simp [right_hom]
 #align semidirect_product.right_hom_inl SemidirectProduct.rightHom_inl
+-/
 
+#print SemidirectProduct.rightHom_inr /-
 @[simp]
 theorem rightHom_inr (g : G) : rightHom (inr g : N ⋊[φ] G) = g := by simp [right_hom]
 #align semidirect_product.right_hom_inr SemidirectProduct.rightHom_inr
+-/
 
+#print SemidirectProduct.rightHom_surjective /-
 theorem rightHom_surjective : Function.Surjective (rightHom : N ⋊[φ] G → G) :=
   Function.surjective_iff_hasRightInverse.2 ⟨inr, rightHom_inr⟩
 #align semidirect_product.right_hom_surjective SemidirectProduct.rightHom_surjective
+-/
 
+#print SemidirectProduct.range_inl_eq_ker_rightHom /-
 theorem range_inl_eq_ker_rightHom : (inl : N →* N ⋊[φ] G).range = rightHom.ker :=
   le_antisymm (fun _ => by simp (config := { contextual := true }) [MonoidHom.mem_ker, eq_comm])
     fun x hx => ⟨x.left, by ext <;> simp_all [MonoidHom.mem_ker]⟩
 #align semidirect_product.range_inl_eq_ker_right_hom SemidirectProduct.range_inl_eq_ker_rightHom
+-/
 
 section lift
 
 variable (f₁ : N →* H) (f₂ : G →* H)
   (h : ∀ g, f₁.comp (φ g).toMonoidHom = (MulAut.conj (f₂ g)).toMonoidHom.comp f₁)
 
+#print SemidirectProduct.lift /-
 /-- Define a group hom `N ⋊[φ] G →* H`, by defining maps `N →* H` and `G →* H`  -/
 def lift (f₁ : N →* H) (f₂ : G →* H)
     (h : ∀ g, f₁.comp (φ g).toMonoidHom = (MulAut.conj (f₂ g)).toMonoidHom.comp f₁) : N ⋊[φ] G →* H
@@ -224,23 +282,33 @@ def lift (f₁ : N →* H) (f₂ : G →* H)
     simp only [MulAut.conj_apply, MonoidHom.comp_apply, MulEquiv.coe_toMonoidHom] at this 
     simp [this, mul_assoc]
 #align semidirect_product.lift SemidirectProduct.lift
+-/
 
+#print SemidirectProduct.lift_inl /-
 @[simp]
 theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
 #align semidirect_product.lift_inl SemidirectProduct.lift_inl
+-/
 
+#print SemidirectProduct.lift_comp_inl /-
 @[simp]
 theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext <;> simp
 #align semidirect_product.lift_comp_inl SemidirectProduct.lift_comp_inl
+-/
 
+#print SemidirectProduct.lift_inr /-
 @[simp]
 theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
 #align semidirect_product.lift_inr SemidirectProduct.lift_inr
+-/
 
+#print SemidirectProduct.lift_comp_inr /-
 @[simp]
 theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
 #align semidirect_product.lift_comp_inr SemidirectProduct.lift_comp_inr
+-/
 
+#print SemidirectProduct.lift_unique /-
 theorem lift_unique (F : N ⋊[φ] G →* H) :
     F = lift (F.comp inl) (F.comp inr) fun _ => by ext <;> simp [inl_aut] :=
   by
@@ -248,12 +316,15 @@ theorem lift_unique (F : N ⋊[φ] G →* H) :
   simp only [lift, MonoidHom.comp_apply, MonoidHom.coe_mk]
   rw [← F.map_mul, inl_left_mul_inr_right]
 #align semidirect_product.lift_unique SemidirectProduct.lift_unique
+-/
 
+#print SemidirectProduct.hom_ext /-
 /-- Two maps out of the semidirect product are equal if they're equal after composition
   with both `inl` and `inr` -/
 theorem hom_ext {f g : N ⋊[φ] G →* H} (hl : f.comp inl = g.comp inl)
     (hr : f.comp inr = g.comp inr) : f = g := by rw [lift_unique f, lift_unique g]; simp only [*]
 #align semidirect_product.hom_ext SemidirectProduct.hom_ext
+-/
 
 end lift
 
@@ -261,6 +332,7 @@ section Map
 
 variable {N₁ : Type _} {G₁ : Type _} [Group N₁] [Group G₁] {φ₁ : G₁ →* MulAut N₁}
 
+#print SemidirectProduct.map /-
 /-- Define a map from `N ⋊[φ] G` to `N₁ ⋊[φ₁] G₁` given maps `N →* N₁` and `G →* G₁` that
   satisfy a commutativity condition `∀ n g, f₁ (φ g n) = φ₁ (f₂ g) (f₁ n)`.  -/
 def map (f₁ : N →* N₁) (f₂ : G →* G₁)
@@ -272,40 +344,55 @@ def map (f₁ : N →* N₁) (f₂ : G →* G₁)
     replace h := MonoidHom.ext_iff.1 (h x.right) y.left
     ext <;> simp_all
 #align semidirect_product.map SemidirectProduct.map
+-/
 
 variable (f₁ : N →* N₁) (f₂ : G →* G₁)
   (h : ∀ g : G, f₁.comp (φ g).toMonoidHom = (φ₁ (f₂ g)).toMonoidHom.comp f₁)
 
+#print SemidirectProduct.map_left /-
 @[simp]
 theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
   rfl
 #align semidirect_product.map_left SemidirectProduct.map_left
+-/
 
+#print SemidirectProduct.map_right /-
 @[simp]
 theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :=
   rfl
 #align semidirect_product.map_right SemidirectProduct.map_right
+-/
 
+#print SemidirectProduct.rightHom_comp_map /-
 @[simp]
 theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom :=
   rfl
 #align semidirect_product.right_hom_comp_map SemidirectProduct.rightHom_comp_map
+-/
 
+#print SemidirectProduct.map_inl /-
 @[simp]
 theorem map_inl (n : N) : map f₁ f₂ h (inl n) = inl (f₁ n) := by simp [map]
 #align semidirect_product.map_inl SemidirectProduct.map_inl
+-/
 
+#print SemidirectProduct.map_comp_inl /-
 @[simp]
 theorem map_comp_inl : (map f₁ f₂ h).comp inl = inl.comp f₁ := by ext <;> simp
 #align semidirect_product.map_comp_inl SemidirectProduct.map_comp_inl
+-/
 
+#print SemidirectProduct.map_inr /-
 @[simp]
 theorem map_inr (g : G) : map f₁ f₂ h (inr g) = inr (f₂ g) := by simp [map]
 #align semidirect_product.map_inr SemidirectProduct.map_inr
+-/
 
+#print SemidirectProduct.map_comp_inr /-
 @[simp]
 theorem map_comp_inr : (map f₁ f₂ h).comp inr = inr.comp f₂ := by ext <;> simp [map]
 #align semidirect_product.map_comp_inr SemidirectProduct.map_comp_inr
+-/
 
 end Map
 

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

@@ -221,7 +221,7 @@ def lift (f₁ : N →* H) (f₂ : G →* H)
   map_one' := by simp
   map_mul' a b := by
     have := fun n g => MonoidHom.ext_iff.1 (h n) g
-    simp only [MulAut.conj_apply, MonoidHom.comp_apply, MulEquiv.coe_toMonoidHom] at this
+    simp only [MulAut.conj_apply, MonoidHom.comp_apply, MulEquiv.coe_toMonoidHom] at this 
     simp [this, mul_assoc]
 #align semidirect_product.lift SemidirectProduct.lift
 

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

@@ -41,12 +41,6 @@ group, semidirect product
 
 variable (N : Type _) (G : Type _) {H : Type _} [Group N] [Group G] [Group H]
 
-/- warning: semidirect_product -> SemidirectProduct is a dubious translation:
-lean 3 declaration is
-  forall (N : Type.{u1}) (G : Type.{u2}) [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G], (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) -> Sort.{max (succ u1) (succ u2)}
-but is expected to have type
-  forall (N : Type.{u1}) (G : Type.{u2}) [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G], (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) -> Sort.{max (succ u1) (succ u2)}
-Case conversion may be inaccurate. Consider using '#align semidirect_product SemidirectProductₓ'. -/
 /-- The semidirect product of groups `N` and `G`, given a map `φ` from `G` to the automorphism
   group of `N`. It the product of sets with the group operation
   `⟨n₁, g₁⟩ * ⟨n₂, g₂⟩ = ⟨n₁ * φ g₁ n₂, g₁ * g₂⟩` -/
@@ -78,72 +72,36 @@ instance : Group (N ⋊[φ] G) where
 instance : Inhabited (N ⋊[φ] G) :=
   ⟨1⟩
 
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 @[simp]
 theorem one_left : (1 : N ⋊[φ] G).left = 1 :=
   rfl
 #align semidirect_product.one_left SemidirectProduct.one_left
 
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 @[simp]
 theorem one_right : (1 : N ⋊[φ] G).right = 1 :=
   rfl
 #align semidirect_product.one_right SemidirectProduct.one_right
 
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 @[simp]
 theorem inv_left (a : N ⋊[φ] G) : a⁻¹.left = φ a.right⁻¹ a.left⁻¹ :=
   rfl
 #align semidirect_product.inv_left SemidirectProduct.inv_left
 
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 @[simp]
 theorem inv_right (a : N ⋊[φ] G) : a⁻¹.right = a.right⁻¹ :=
   rfl
 #align semidirect_product.inv_right SemidirectProduct.inv_right
 
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 @[simp]
 theorem mul_left (a b : N ⋊[φ] G) : (a * b).left = a.left * φ a.right b.left :=
   rfl
 #align semidirect_product.mul_left SemidirectProduct.mul_left
 
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 @[simp]
 theorem mul_right (a b : N ⋊[φ] G) : (a * b).right = a.right * b.right :=
   rfl
 #align semidirect_product.mul_right SemidirectProduct.mul_right
 
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 /-- The canonical map `N →* N ⋊[φ] G` sending `n` to `⟨n, 1⟩` -/
 def inl : N →* N ⋊[φ] G where
   toFun n := ⟨n, 1⟩
@@ -151,52 +109,25 @@ def inl : N →* N ⋊[φ] G where
   map_mul' := by intros <;> ext <;> simp
 #align semidirect_product.inl SemidirectProduct.inl
 
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 @[simp]
 theorem left_inl (n : N) : (inl n : N ⋊[φ] G).left = n :=
   rfl
 #align semidirect_product.left_inl SemidirectProduct.left_inl
 
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 @[simp]
 theorem right_inl (n : N) : (inl n : N ⋊[φ] G).right = 1 :=
   rfl
 #align semidirect_product.right_inl SemidirectProduct.right_inl
 
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 theorem inl_injective : Function.Injective (inl : N → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨left, left_inl⟩
 #align semidirect_product.inl_injective SemidirectProduct.inl_injective
 
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 @[simp]
 theorem inl_inj {n₁ n₂ : N} : (inl n₁ : N ⋊[φ] G) = inl n₂ ↔ n₁ = n₂ :=
   inl_injective.eq_iff
 #align semidirect_product.inl_inj SemidirectProduct.inl_inj
 
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 /-- The canonical map `G →* N ⋊[φ] G` sending `g` to `⟨1, g⟩` -/
 def inr : G →* N ⋊[φ] G where
   toFun g := ⟨1, g⟩
@@ -204,80 +135,41 @@ def inr : G →* N ⋊[φ] G where
   map_mul' := by intros <;> ext <;> simp
 #align semidirect_product.inr SemidirectProduct.inr
 
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 @[simp]
 theorem left_inr (g : G) : (inr g : N ⋊[φ] G).left = 1 :=
   rfl
 #align semidirect_product.left_inr SemidirectProduct.left_inr
 
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 @[simp]
 theorem right_inr (g : G) : (inr g : N ⋊[φ] G).right = g :=
   rfl
 #align semidirect_product.right_inr SemidirectProduct.right_inr
 
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 theorem inr_injective : Function.Injective (inr : G → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨right, right_inr⟩
 #align semidirect_product.inr_injective SemidirectProduct.inr_injective
 
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 @[simp]
 theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ = g₂ :=
   inr_injective.eq_iff
 #align semidirect_product.inr_inj SemidirectProduct.inr_inj
 
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 theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n * inr g⁻¹ := by
   ext <;> simp
 #align semidirect_product.inl_aut SemidirectProduct.inl_aut
 
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 theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr g⁻¹ * inl n * inr g := by
   rw [← MonoidHom.map_inv, inl_aut, inv_inv]
 #align semidirect_product.inl_aut_inv SemidirectProduct.inl_aut_inv
 
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 @[simp]
 theorem mk_eq_inl_mul_inr (g : G) (n : N) : (⟨n, g⟩ : N ⋊[φ] G) = inl n * inr g := by ext <;> simp
 #align semidirect_product.mk_eq_inl_mul_inr SemidirectProduct.mk_eq_inl_mul_inr
 
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 @[simp]
 theorem inl_left_mul_inr_right (x : N ⋊[φ] G) : inl x.left * inr x.right = x := by ext <;> simp
 #align semidirect_product.inl_left_mul_inr_right SemidirectProduct.inl_left_mul_inr_right
 
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 /-- The canonical projection map `N ⋊[φ] G →* G`, as a group hom. -/
 def rightHom : N ⋊[φ] G →* G where
   toFun := SemidirectProduct.right
@@ -285,68 +177,32 @@ def rightHom : N ⋊[φ] G →* G where
   map_mul' _ _ := rfl
 #align semidirect_product.right_hom SemidirectProduct.rightHom
 
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 @[simp]
 theorem rightHom_eq_right : (rightHom : N ⋊[φ] G → G) = right :=
   rfl
 #align semidirect_product.right_hom_eq_right SemidirectProduct.rightHom_eq_right
 
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 @[simp]
 theorem rightHom_comp_inl : (rightHom : N ⋊[φ] G →* G).comp inl = 1 := by ext <;> simp [right_hom]
 #align semidirect_product.right_hom_comp_inl SemidirectProduct.rightHom_comp_inl
 
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 @[simp]
 theorem rightHom_comp_inr : (rightHom : N ⋊[φ] G →* G).comp inr = MonoidHom.id _ := by
   ext <;> simp [right_hom]
 #align semidirect_product.right_hom_comp_inr SemidirectProduct.rightHom_comp_inr
 
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 @[simp]
 theorem rightHom_inl (n : N) : rightHom (inl n : N ⋊[φ] G) = 1 := by simp [right_hom]
 #align semidirect_product.right_hom_inl SemidirectProduct.rightHom_inl
 
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 @[simp]
 theorem rightHom_inr (g : G) : rightHom (inr g : N ⋊[φ] G) = g := by simp [right_hom]
 #align semidirect_product.right_hom_inr SemidirectProduct.rightHom_inr
 
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 theorem rightHom_surjective : Function.Surjective (rightHom : N ⋊[φ] G → G) :=
   Function.surjective_iff_hasRightInverse.2 ⟨inr, rightHom_inr⟩
 #align semidirect_product.right_hom_surjective SemidirectProduct.rightHom_surjective
 
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 theorem range_inl_eq_ker_rightHom : (inl : N →* N ⋊[φ] G).range = rightHom.ker :=
   le_antisymm (fun _ => by simp (config := { contextual := true }) [MonoidHom.mem_ker, eq_comm])
     fun x hx => ⟨x.left, by ext <;> simp_all [MonoidHom.mem_ker]⟩
@@ -357,9 +213,6 @@ section lift
 variable (f₁ : N →* H) (f₂ : G →* H)
   (h : ∀ g, f₁.comp (φ g).toMonoidHom = (MulAut.conj (f₂ g)).toMonoidHom.comp f₁)
 
-/- warning: semidirect_product.lift -> SemidirectProduct.lift is a dubious translation:
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 /-- Define a group hom `N ⋊[φ] G →* H`, by defining maps `N →* H` and `G →* H`  -/
 def lift (f₁ : N →* H) (f₂ : G →* H)
     (h : ∀ g, f₁.comp (φ g).toMonoidHom = (MulAut.conj (f₂ g)).toMonoidHom.comp f₁) : N ⋊[φ] G →* H
@@ -372,37 +225,22 @@ def lift (f₁ : N →* H) (f₂ : G →* H)
     simp [this, mul_assoc]
 #align semidirect_product.lift SemidirectProduct.lift
 
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 @[simp]
 theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
 #align semidirect_product.lift_inl SemidirectProduct.lift_inl
 
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 @[simp]
 theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext <;> simp
 #align semidirect_product.lift_comp_inl SemidirectProduct.lift_comp_inl
 
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 @[simp]
 theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
 #align semidirect_product.lift_inr SemidirectProduct.lift_inr
 
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 @[simp]
 theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
 #align semidirect_product.lift_comp_inr SemidirectProduct.lift_comp_inr
 
-/- warning: semidirect_product.lift_unique -> SemidirectProduct.lift_unique is a dubious translation:
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 theorem lift_unique (F : N ⋊[φ] G →* H) :
     F = lift (F.comp inl) (F.comp inr) fun _ => by ext <;> simp [inl_aut] :=
   by
@@ -411,9 +249,6 @@ theorem lift_unique (F : N ⋊[φ] G →* H) :
   rw [← F.map_mul, inl_left_mul_inr_right]
 #align semidirect_product.lift_unique SemidirectProduct.lift_unique
 
-/- warning: semidirect_product.hom_ext -> SemidirectProduct.hom_ext is a dubious translation:
-<too large>
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 /-- Two maps out of the semidirect product are equal if they're equal after composition
   with both `inl` and `inr` -/
 theorem hom_ext {f g : N ⋊[φ] G →* H} (hl : f.comp inl = g.comp inl)
@@ -426,9 +261,6 @@ section Map
 
 variable {N₁ : Type _} {G₁ : Type _} [Group N₁] [Group G₁] {φ₁ : G₁ →* MulAut N₁}
 
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 /-- Define a map from `N ⋊[φ] G` to `N₁ ⋊[φ₁] G₁` given maps `N →* N₁` and `G →* G₁` that
   satisfy a commutativity condition `∀ n g, f₁ (φ g n) = φ₁ (f₂ g) (f₁ n)`.  -/
 def map (f₁ : N →* N₁) (f₂ : G →* G₁)
@@ -444,54 +276,33 @@ def map (f₁ : N →* N₁) (f₂ : G →* G₁)
 variable (f₁ : N →* N₁) (f₂ : G →* G₁)
   (h : ∀ g : G, f₁.comp (φ g).toMonoidHom = (φ₁ (f₂ g)).toMonoidHom.comp f₁)
 
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 @[simp]
 theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
   rfl
 #align semidirect_product.map_left SemidirectProduct.map_left
 
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 @[simp]
 theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :=
   rfl
 #align semidirect_product.map_right SemidirectProduct.map_right
 
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 @[simp]
 theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom :=
   rfl
 #align semidirect_product.right_hom_comp_map SemidirectProduct.rightHom_comp_map
 
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 @[simp]
 theorem map_inl (n : N) : map f₁ f₂ h (inl n) = inl (f₁ n) := by simp [map]
 #align semidirect_product.map_inl SemidirectProduct.map_inl
 
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 @[simp]
 theorem map_comp_inl : (map f₁ f₂ h).comp inl = inl.comp f₁ := by ext <;> simp
 #align semidirect_product.map_comp_inl SemidirectProduct.map_comp_inl
 
-/- warning: semidirect_product.map_inr -> SemidirectProduct.map_inr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align semidirect_product.map_inr SemidirectProduct.map_inrₓ'. -/
 @[simp]
 theorem map_inr (g : G) : map f₁ f₂ h (inr g) = inr (f₂ g) := by simp [map]
 #align semidirect_product.map_inr SemidirectProduct.map_inr
 
-/- warning: semidirect_product.map_comp_inr -> SemidirectProduct.map_comp_inr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align semidirect_product.map_comp_inr SemidirectProduct.map_comp_inrₓ'. -/
 @[simp]
 theorem map_comp_inr : (map f₁ f₂ h).comp inr = inr.comp f₂ := by ext <;> simp [map]
 #align semidirect_product.map_comp_inr SemidirectProduct.map_comp_inr

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

@@ -417,10 +417,7 @@ Case conversion may be inaccurate. Consider using '#align semidirect_product.hom
 /-- Two maps out of the semidirect product are equal if they're equal after composition
   with both `inl` and `inr` -/
 theorem hom_ext {f g : N ⋊[φ] G →* H} (hl : f.comp inl = g.comp inl)
-    (hr : f.comp inr = g.comp inr) : f = g :=
-  by
-  rw [lift_unique f, lift_unique g]
-  simp only [*]
+    (hr : f.comp inr = g.comp inr) : f = g := by rw [lift_unique f, lift_unique g]; simp only [*]
 #align semidirect_product.hom_ext SemidirectProduct.hom_ext
 
 end lift

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

@@ -101,10 +101,7 @@ theorem one_right : (1 : N ⋊[φ] G).right = 1 :=
 #align semidirect_product.one_right SemidirectProduct.one_right
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inv_left SemidirectProduct.inv_leftₓ'. -/
 @[simp]
 theorem inv_left (a : N ⋊[φ] G) : a⁻¹.left = φ a.right⁻¹ a.left⁻¹ :=
@@ -123,10 +120,7 @@ theorem inv_right (a : N ⋊[φ] G) : a⁻¹.right = a.right⁻¹ :=
 #align semidirect_product.inv_right SemidirectProduct.inv_right
 
 /- warning: semidirect_product.mul_left -> SemidirectProduct.mul_left is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.mul_left SemidirectProduct.mul_leftₓ'. -/
 @[simp]
 theorem mul_left (a b : N ⋊[φ] G) : (a * b).left = a.left * φ a.right b.left :=
@@ -190,10 +184,7 @@ theorem inl_injective : Function.Injective (inl : N → N ⋊[φ] G) :=
 #align semidirect_product.inl_injective SemidirectProduct.inl_injective
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_inj SemidirectProduct.inl_injₓ'. -/
 @[simp]
 theorem inl_inj {n₁ n₂ : N} : (inl n₁ : N ⋊[φ] G) = inl n₂ ↔ n₁ = n₂ :=
@@ -246,10 +237,7 @@ theorem inr_injective : Function.Injective (inr : G → N ⋊[φ] G) :=
 #align semidirect_product.inr_injective SemidirectProduct.inr_injective
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inr_inj SemidirectProduct.inr_injₓ'. -/
 @[simp]
 theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ = g₂ :=
@@ -257,40 +245,28 @@ theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ =
 #align semidirect_product.inr_inj SemidirectProduct.inr_inj
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut SemidirectProduct.inl_autₓ'. -/
 theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n * inr g⁻¹ := by
   ext <;> simp
 #align semidirect_product.inl_aut SemidirectProduct.inl_aut
 
 /- warning: semidirect_product.inl_aut_inv -> SemidirectProduct.inl_aut_inv is a dubious translation:
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(MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut_inv SemidirectProduct.inl_aut_invₓ'. -/
 theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr g⁻¹ * inl n * inr g := by
   rw [← MonoidHom.map_inv, inl_aut, inv_inv]
 #align semidirect_product.inl_aut_inv SemidirectProduct.inl_aut_inv
 
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 Case conversion may be inaccurate. Consider using '#align semidirect_product.mk_eq_inl_mul_inr SemidirectProduct.mk_eq_inl_mul_inrₓ'. -/
 @[simp]
 theorem mk_eq_inl_mul_inr (g : G) (n : N) : (⟨n, g⟩ : N ⋊[φ] G) = inl n * inr g := by ext <;> simp
 #align semidirect_product.mk_eq_inl_mul_inr SemidirectProduct.mk_eq_inl_mul_inr
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_left_mul_inr_right SemidirectProduct.inl_left_mul_inr_rightₓ'. -/
 @[simp]
 theorem inl_left_mul_inr_right (x : N ⋊[φ] G) : inl x.left * inr x.right = x := by ext <;> simp
@@ -342,20 +318,14 @@ theorem rightHom_comp_inr : (rightHom : N ⋊[φ] G →* G).comp inr = MonoidHom
 #align semidirect_product.right_hom_comp_inr SemidirectProduct.rightHom_comp_inr
 
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 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_inl SemidirectProduct.rightHom_inlₓ'. -/
 @[simp]
 theorem rightHom_inl (n : N) : rightHom (inl n : N ⋊[φ] G) = 1 := by simp [right_hom]
 #align semidirect_product.right_hom_inl SemidirectProduct.rightHom_inl
 
 /- warning: semidirect_product.right_hom_inr -> SemidirectProduct.rightHom_inr is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_inr SemidirectProduct.rightHom_inrₓ'. -/
 @[simp]
 theorem rightHom_inr (g : G) : rightHom (inr g : N ⋊[φ] G) = g := by simp [right_hom]
@@ -388,10 +358,7 @@ variable (f₁ : N →* H) (f₂ : G →* H)
   (h : ∀ g, f₁.comp (φ g).toMonoidHom = (MulAut.conj (f₂ g)).toMonoidHom.comp f₁)
 
 /- warning: semidirect_product.lift -> SemidirectProduct.lift is a dubious translation:
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_inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (FunLike.coe.{succ u3, succ u3, succ u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun 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G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun 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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift SemidirectProduct.liftₓ'. -/
 /-- Define a group hom `N ⋊[φ] G →* H`, by defining maps `N →* H` and `G →* H`  -/
 def lift (f₁ : N →* H) (f₂ : G →* H)
@@ -406,50 +373,35 @@ def lift (f₁ : N →* H) (f₂ : G →* H)
 #align semidirect_product.lift SemidirectProduct.lift
 
 /- warning: semidirect_product.lift_inl -> SemidirectProduct.lift_inl is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_inl SemidirectProduct.lift_inlₓ'. -/
 @[simp]
 theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
 #align semidirect_product.lift_inl SemidirectProduct.lift_inl
 
 /- warning: semidirect_product.lift_comp_inl -> SemidirectProduct.lift_comp_inl is a dubious translation:
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_inst_1))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u3, u2, u2} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) => MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3)))) (MulOneClass.toMul.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_comp_inl SemidirectProduct.lift_comp_inlₓ'. -/
 @[simp]
 theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext <;> simp
 #align semidirect_product.lift_comp_inl SemidirectProduct.lift_comp_inl
 
 /- warning: semidirect_product.lift_inr -> SemidirectProduct.lift_inr is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_inr SemidirectProduct.lift_inrₓ'. -/
 @[simp]
 theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
 #align semidirect_product.lift_inr SemidirectProduct.lift_inr
 
 /- warning: semidirect_product.lift_comp_inr -> SemidirectProduct.lift_comp_inr is a dubious translation:
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_inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u2, u2} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) => MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3)))) (MulOneClass.toMul.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_comp_inr SemidirectProduct.lift_comp_inrₓ'. -/
 @[simp]
 theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
 #align semidirect_product.lift_comp_inr SemidirectProduct.lift_comp_inr
 
 /- warning: semidirect_product.lift_unique -> SemidirectProduct.lift_unique is a dubious translation:
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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u3, u3, u2} (MonoidHom.{u3, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) 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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u3, u2} (MonoidHom.{u3, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ _x))) (MonoidHom.comp.{u2, u1, u1} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (MulEquiv.toMonoidHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (MulAut.instGroupMulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (fun (_x_1 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) => MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) _x_1) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (MulAut.instGroupMulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun 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_inst_3))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))))) (MulAut.instGroupMulAut.{u1} ((fun 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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_unique SemidirectProduct.lift_uniqueₓ'. -/
 theorem lift_unique (F : N ⋊[φ] G →* H) :
     F = lift (F.comp inl) (F.comp inr) fun _ => by ext <;> simp [inl_aut] :=
@@ -460,10 +412,7 @@ theorem lift_unique (F : N ⋊[φ] G →* H) :
 #align semidirect_product.lift_unique SemidirectProduct.lift_unique
 
 /- warning: semidirect_product.hom_ext -> SemidirectProduct.hom_ext is a dubious translation:
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(DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {f : MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))} {g : MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) 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(SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u2, max u1 u2, u3} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.hom_ext SemidirectProduct.hom_extₓ'. -/
 /-- Two maps out of the semidirect product are equal if they're equal after composition
   with both `inl` and `inr` -/
@@ -481,10 +430,7 @@ section Map
 variable {N₁ : Type _} {G₁ : Type _} [Group N₁] [Group G₁] {φ₁ : G₁ →* MulAut N₁}
 
 /- warning: semidirect_product.map -> SemidirectProduct.map is a dubious translation:
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(MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, max u4 u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map SemidirectProduct.mapₓ'. -/
 /-- Define a map from `N ⋊[φ] G` to `N₁ ⋊[φ₁] G₁` given maps `N →* N₁` and `G →* G₁` that
   satisfy a commutativity condition `∀ n g, f₁ (φ g n) = φ₁ (f₂ g) (f₁ n)`.  -/
@@ -502,10 +448,7 @@ variable (f₁ : N →* N₁) (f₂ : G →* G₁)
   (h : ∀ g : G, f₁.comp (φ g).toMonoidHom = (φ₁ (f₂ g)).toMonoidHom.comp f₁)
 
 /- warning: semidirect_product.map_left -> SemidirectProduct.map_left is a dubious translation:
-lean 3 declaration is
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(Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_left SemidirectProduct.map_leftₓ'. -/
 @[simp]
 theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
@@ -513,10 +456,7 @@ theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
 #align semidirect_product.map_left SemidirectProduct.map_left
 
 /- warning: semidirect_product.map_right -> SemidirectProduct.map_right is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_right SemidirectProduct.map_rightₓ'. -/
 @[simp]
 theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :=
@@ -524,10 +464,7 @@ theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :
 #align semidirect_product.map_right SemidirectProduct.map_right
 
 /- warning: semidirect_product.right_hom_comp_map -> SemidirectProduct.rightHom_comp_map is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_comp_map SemidirectProduct.rightHom_comp_mapₓ'. -/
 @[simp]
 theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom :=
@@ -535,40 +472,28 @@ theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom
 #align semidirect_product.right_hom_comp_map SemidirectProduct.rightHom_comp_map
 
 /- warning: semidirect_product.map_inl -> SemidirectProduct.map_inl is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_inl SemidirectProduct.map_inlₓ'. -/
 @[simp]
 theorem map_inl (n : N) : map f₁ f₂ h (inl n) = inl (f₁ n) := by simp [map]
 #align semidirect_product.map_inl SemidirectProduct.map_inl
 
 /- warning: semidirect_product.map_comp_inl -> SemidirectProduct.map_comp_inl is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_comp_inl SemidirectProduct.map_comp_inlₓ'. -/
 @[simp]
 theorem map_comp_inl : (map f₁ f₂ h).comp inl = inl.comp f₁ := by ext <;> simp
 #align semidirect_product.map_comp_inl SemidirectProduct.map_comp_inl
 
 /- warning: semidirect_product.map_inr -> SemidirectProduct.map_inr is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_inr SemidirectProduct.map_inrₓ'. -/
 @[simp]
 theorem map_inr (g : G) : map f₁ f₂ h (inr g) = inr (f₂ g) := by simp [map]
 #align semidirect_product.map_inr SemidirectProduct.map_inr
 
 /- warning: semidirect_product.map_comp_inr -> SemidirectProduct.map_comp_inr is a dubious translation:
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G₁ _inst_5))) (MonoidHom.monoidHomClass.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} G (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u1 u4, max u3 u2} G (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u4, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inr.{u1, u4} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u2, max u3 u2} G G₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
+<too large>
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_comp_inr SemidirectProduct.map_comp_inrₓ'. -/
 @[simp]
 theorem map_comp_inr : (map f₁ f₂ h).comp inr = inr.comp f₂ := by ext <;> simp [map]

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

@@ -104,7 +104,7 @@ theorem one_right : (1 : N ⋊[φ] G).right = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (a : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (Inv.inv.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toHasInv.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))) a)) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ (Inv.inv.{u2} G (DivInvMonoid.toHasInv.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u1} N (DivInvMonoid.toHasInv.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ a)))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (Inv.inv.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instInvSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u2} N (InvOneClass.toInv.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1)))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a)))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (Inv.inv.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instInvSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u2} N (InvOneClass.toInv.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1)))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inv_left SemidirectProduct.inv_leftₓ'. -/
 @[simp]
 theorem inv_left (a : N ⋊[φ] G) : a⁻¹.left = φ a.right⁻¹ a.left⁻¹ :=
@@ -126,7 +126,7 @@ theorem inv_right (a : N ⋊[φ] G) : a⁻¹.right = a.right⁻¹ :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (a : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) a b)) (HMul.hMul.{u1, u1, u1} N N N (instHMul.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ a) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ b)))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) a b)) (HMul.hMul.{u2, u2, u2} N ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)) N (instHMul.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a) (FunLike.coe.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) a b)) (HMul.hMul.{u2, u2, u2} N ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)) N (instHMul.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a) (FunLike.coe.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.mul_left SemidirectProduct.mul_leftₓ'. -/
 @[simp]
 theorem mul_left (a b : N ⋊[φ] G) : (a * b).left = a.left * φ a.right b.left :=
@@ -161,7 +161,7 @@ def inl : N →* N ⋊[φ] G where
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) n
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (n : N), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) n
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (n : N), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) n
 Case conversion may be inaccurate. Consider using '#align semidirect_product.left_inl SemidirectProduct.left_inlₓ'. -/
 @[simp]
 theorem left_inl (n : N) : (inl n : N ⋊[φ] G).left = n :=
@@ -172,7 +172,7 @@ theorem left_inl (n : N) : (inl n : N ⋊[φ] G).left = n :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (One.toOfNat1.{u2} G (InvOneClass.toOne.{u2} G (DivInvOneMonoid.toInvOneClass.{u2} G (DivisionMonoid.toDivInvOneMonoid.{u2} G (Group.toDivisionMonoid.{u2} G _inst_2))))))
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (One.toOfNat1.{u2} G (InvOneClass.toOne.{u2} G (DivInvOneMonoid.toInvOneClass.{u2} G (DivisionMonoid.toDivInvOneMonoid.{u2} G (Group.toDivisionMonoid.{u2} G _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_inl SemidirectProduct.right_inlₓ'. -/
 @[simp]
 theorem right_inl (n : N) : (inl n : N ⋊[φ] G).right = 1 :=
@@ -183,7 +183,7 @@ theorem right_inl (n : N) : (inl n : N ⋊[φ] G).right = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u1, max (succ u1) (succ u2)} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u2) (succ u1)} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u2) (succ u1)} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_injective SemidirectProduct.inl_injectiveₓ'. -/
 theorem inl_injective : Function.Injective (inl : N → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨left, left_inl⟩
@@ -193,7 +193,7 @@ theorem inl_injective : Function.Injective (inl : N → N ⋊[φ] G) :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {n₁ : N} {n₂ : N}, Iff (Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n₁) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n₂)) (Eq.{succ u1} N n₁ n₂)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {n₁ : N} {n₂ : N}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₂)) (Eq.{succ u2} N n₁ n₂)
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {n₁ : N} {n₂ : N}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₂)) (Eq.{succ u2} N n₁ n₂)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_inj SemidirectProduct.inl_injₓ'. -/
 @[simp]
 theorem inl_inj {n₁ n₂ : N} : (inl n₁ : N ⋊[φ] G) = inl n₂ ↔ n₁ = n₂ :=
@@ -217,7 +217,7 @@ def inr : G →* N ⋊[φ] G where
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) (OfNat.ofNat.{u1} N 1 (OfNat.mk.{u1} N 1 (One.one.{u1} N (MulOneClass.toHasOne.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (InvOneClass.toOne.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1))))))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (InvOneClass.toOne.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.left_inr SemidirectProduct.left_inrₓ'. -/
 @[simp]
 theorem left_inr (g : G) : (inr g : N ⋊[φ] G).left = 1 :=
@@ -228,7 +228,7 @@ theorem left_inr (g : G) : (inr g : N ⋊[φ] G).left = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_inr SemidirectProduct.right_inrₓ'. -/
 @[simp]
 theorem right_inr (g : G) : (inr g : N ⋊[φ] G).right = g :=
@@ -239,7 +239,7 @@ theorem right_inr (g : G) : (inr g : N ⋊[φ] G).right = g :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u1) (succ u2)} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u1) (succ u2)} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u1) (succ u2)} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inr_injective SemidirectProduct.inr_injectiveₓ'. -/
 theorem inr_injective : Function.Injective (inr : G → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨right, right_inr⟩
@@ -249,7 +249,7 @@ theorem inr_injective : Function.Injective (inr : G → N ⋊[φ] G) :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {g₁ : G} {g₂ : G}, Iff (Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g₁) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g₂)) (Eq.{succ u2} G g₁ g₂)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {g₁ : G} {g₂ : G}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 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(Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G 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(SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g₂)) (Eq.{succ u1} G g₁ g₂)
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {g₁ : G} {g₂ : G}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g₂)) (Eq.{succ u1} G g₁ g₂)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inr_inj SemidirectProduct.inr_injₓ'. -/
 @[simp]
 theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ = g₂ :=
@@ -260,7 +260,7 @@ theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ =
 lean 3 declaration is
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 but is expected to have type
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(DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} 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(DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N 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(Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut SemidirectProduct.inl_autₓ'. -/
 theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n * inr g⁻¹ := by
   ext <;> simp
@@ -270,7 +270,7 @@ theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n *
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) 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_inst_2 φ) g))
 but is expected to have type
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(Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) => SemidirectProduct.{u2, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) G _inst_1 _inst_2 φ) (FunLike.coe.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N (fun (a : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) a) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (InvOneClass.toInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (DivInvOneMonoid.toInvOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) 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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (a : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) a) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N 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(MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 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(Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N 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(MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (InvOneClass.toInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (DivInvOneMonoid.toInvOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) 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(SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} 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 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut_inv SemidirectProduct.inl_aut_invₓ'. -/
 theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr g⁻¹ * inl n * inr g := by
   rw [← MonoidHom.map_inv, inl_aut, inv_inv]
@@ -280,7 +280,7 @@ theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.mk.{u1, u2} N G _inst_1 _inst_2 φ n g) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u2) (succ u1)} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.mk.{u2, u1} N G _inst_1 _inst_2 φ n g) (HMul.hMul.{max u2 u1, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u2) (succ u1)} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.mk.{u2, u1} N G _inst_1 _inst_2 φ n g) (HMul.hMul.{max u2 u1, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.mk_eq_inl_mul_inr SemidirectProduct.mk_eq_inl_mul_inrₓ'. -/
 @[simp]
 theorem mk_eq_inl_mul_inr (g : G) (n : N) : (⟨n, g⟩ : N ⋊[φ] G) = inl n * inr g := by ext <;> simp
@@ -290,7 +290,7 @@ theorem mk_eq_inl_mul_inr (g : G) (n : N) : (⟨n, g⟩ : N ⋊[φ] G) = inl n *
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ (max u1 u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ x)) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ x))) x
 but is expected to have type
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(Group.toDivInvMonoid.{u2} N _inst_1))))))))} (x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{max (succ u2) (succ u1)} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (HMul.hMul.{max u2 u1, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ x)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ x)) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ x)) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, 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(SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ x))) x
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(Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ x)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ x))) x
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_left_mul_inr_right SemidirectProduct.inl_left_mul_inr_rightₓ'. -/
 @[simp]
 theorem inl_left_mul_inr_right (x : N ⋊[φ] G) : inl x.left * inr x.right = x := by ext <;> simp
@@ -313,7 +313,7 @@ def rightHom : N ⋊[φ] G →* G where
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Eq.{max (succ u1) (succ u2)} ((fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ)) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ)) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Eq.{max (succ u2) (succ u1)} (forall (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ)) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ)
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Eq.{max (succ u2) (succ u1)} (forall (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ)) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_eq_right SemidirectProduct.rightHom_eq_rightₓ'. -/
 @[simp]
 theorem rightHom_eq_right : (rightHom : N ⋊[φ] G → G) = right :=
@@ -345,7 +345,7 @@ theorem rightHom_comp_inr : (rightHom : N ⋊[φ] G →* G).comp inr = MonoidHom
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (a : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G 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u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (a : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (Group.toDivisionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (a : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_inl SemidirectProduct.rightHom_inlₓ'. -/
 @[simp]
 theorem rightHom_inl (n : N) : rightHom (inl n : N ⋊[φ] G) = 1 := by simp [right_hom]
@@ -355,7 +355,7 @@ theorem rightHom_inl (n : N) : rightHom (inl n : N ⋊[φ] G) = 1 := by simp [ri
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 but is expected to have type
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(Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (a : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G 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(SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) 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(DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_inr SemidirectProduct.rightHom_inrₓ'. -/
 @[simp]
 theorem rightHom_inr (g : G) : rightHom (inr g : N ⋊[φ] G) = g := by simp [right_hom]
@@ -365,7 +365,7 @@ theorem rightHom_inr (g : G) : rightHom (inr g : N ⋊[φ] G) = g := by simp [ri
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Surjective.{max (succ u1) (succ u2), succ u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Surjective.{max (succ u2) (succ u1), succ u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Surjective.{max (succ u2) (succ u1), succ u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_surjective SemidirectProduct.rightHom_surjectiveₓ'. -/
 theorem rightHom_surjective : Function.Surjective (rightHom : N ⋊[φ] G → G) :=
   Function.surjective_iff_hasRightInverse.2 ⟨inr, rightHom_inr⟩
@@ -391,7 +391,7 @@ variable (f₁ : N →* H) (f₂ : G →* H)
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), (forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N H H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} H H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) (MonoidHom.hasCoeToFun.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)) -> (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N 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_inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u3, u3} ((fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))
+  forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))))))) (MonoidHomClass.toMulHomClass.{u3, u3, u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift SemidirectProduct.liftₓ'. -/
 /-- Define a group hom `N ⋊[φ] G →* H`, by defining maps `N →* H` and `G →* H`  -/
 def lift (f₁ : N →* H) (f₂ : G →* H)
@@ -409,7 +409,7 @@ def lift (f₁ : N →* H) (f₂ : G →* H)
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, 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 but is expected to have type
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(Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (FunLike.coe.{succ u3, succ u3, succ u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) => MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) _x) (MulHomClass.toFunLike.{u3, u3, u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) 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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₁ n)
+  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N 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(Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (FunLike.coe.{succ u3, succ u3, succ u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun 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G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun 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_inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => H) _x) (MulHomClass.toFunLike.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{max u2 u1, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) (SemidirectProduct.lift.{u2, u1, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => H) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N H (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₁ n)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_inl SemidirectProduct.lift_inlₓ'. -/
 @[simp]
 theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
@@ -419,7 +419,7 @@ theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, 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(Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) f₁
 but is expected to have type
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(DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))} (f₁ : MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, u3, u2} N N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u3, u3} N N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N 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_inst_1))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) 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(Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u3, u2, u2} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun 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G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3)))) (MulOneClass.toMul.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u3 u1, u2} N (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u3, u1, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inl.{u3, u1} N G _inst_1 _inst_2 φ)) f₁
+  forall {N : Type.{u3}} {G : Type.{u1}} {H : Type.{u2}} [_inst_1 : Group.{u3} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u2} H] {φ : MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))} (f₁ : MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, u3, u2} N N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N 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(Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N 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: G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => 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G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3)))) (MulOneClass.toMul.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))))))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u3 u1, u2} N (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u3, u1, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inl.{u3, u1} N G _inst_1 _inst_2 φ)) f₁
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_comp_inl SemidirectProduct.lift_comp_inlₓ'. -/
 @[simp]
 theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext <;> simp
@@ -429,7 +429,7 @@ theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext <;> simp
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, 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 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N 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(DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 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(MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g)
+  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) => (fun 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(MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => H) _x) (MulHomClass.toFunLike.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} 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(Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{max u2 u1, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) (SemidirectProduct.lift.{u2, u1, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G 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(SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_inr SemidirectProduct.lift_inrₓ'. -/
 @[simp]
 theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
@@ -439,7 +439,7 @@ theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} 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(Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, max u1 u2, u3} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) f₂
 but is expected to have type
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(DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u1) (succ u2)} (MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u1, u1, u2} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u2, u2} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) => MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) 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(Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u1 u3, u2} G (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u1, u3, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inr.{u1, u3} N G _inst_1 _inst_2 φ)) f₂
+  forall {N : Type.{u1}} {G : Type.{u3}} {H : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u3} G] [_inst_3 : Group.{u2} H] {φ : MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u1) (succ u2)} (MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u1, u1, u2} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u1 u3, u2} G (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u1, u3, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inr.{u1, u3} N G _inst_1 _inst_2 φ)) f₂
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_comp_inr SemidirectProduct.lift_comp_inrₓ'. -/
 @[simp]
 theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
@@ -449,7 +449,7 @@ theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (F : MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), Eq.{max (succ u3) (succ (max u1 u2))} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) F (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u2, max u1 u2, u3} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) (fun (_x : G) => MonoidHom.ext.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) _x)))))) trivial)))
 but is expected to have type
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G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHom.monoidHomClass.{u3, max u2 u3} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u3} N G _inst_1 _inst_2 φ) _x)))))))))
+  forall {N : Type.{u2}} {G : Type.{u3}} {H : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u3} G] [_inst_3 : Group.{u1} H] {φ : MonoidHom.{u3, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (F : MonoidHom.{max u3 u2, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))), Eq.{max (max (succ u2) (succ u3)) (succ u1)} (MonoidHom.{max u3 u2, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) F (SemidirectProduct.lift.{u2, u3, u1} N G H _inst_1 _inst_2 _inst_3 φ (MonoidHom.comp.{u2, max u2 u3, u1} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3))) F (SemidirectProduct.inl.{u2, u3} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u3, max u2 u3, u1} G (SemidirectProduct.{u2, 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(Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3))) (MonoidHom.comp.{u2, max u2 u3, u1} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3))) F (SemidirectProduct.inl.{u2, u3} N G _inst_1 _inst_2 φ)) (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (MonoidHom.{u3, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u3, u3, u2} (MonoidHom.{u3, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) 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(Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ _x))) (MonoidHom.comp.{u2, u1, u1} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (MulEquiv.toMonoidHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => H) _x) _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) 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(DivisionMonoid.toDivInvMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3)))) (MonoidHom.monoidHomClass.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))))) F (FunLike.coe.{succ (max u2 u3), succ u3, succ (max u2 u3)} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (fun (a : G) => SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (MulHomClass.toFunLike.{max u2 u3, u3, max u2 u3} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u3, max u2 u3} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHom.monoidHomClass.{u3, max u2 u3} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u3} N G _inst_1 _inst_2 φ) _x)))))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_unique SemidirectProduct.lift_uniqueₓ'. -/
 theorem lift_unique (F : N ⋊[φ] G →* H) :
     F = lift (F.comp inl) (F.comp inr) fun _ => by ext <;> simp [inl_aut] :=
@@ -484,7 +484,7 @@ variable {N₁ : Type _} {G₁ : Type _} [Group N₁] [Group G₁] {φ₁ : G₁
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))), (forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)) -> (MonoidHom.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₁) => MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u3 u4, u4, u3} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u3 u4, u4, u3} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, max u4 u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, max u4 u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map SemidirectProduct.mapₓ'. -/
 /-- Define a map from `N ⋊[φ] G` to `N₁ ⋊[φ₁] G₁` given maps `N →* N₁` and `G →* G₁` that
   satisfy a commutativity condition `∀ n g, f₁ (φ g n) = φ₁ (f₂ g) (f₁ n)`.  -/
@@ -505,7 +505,7 @@ variable (f₁ : N →* N₁) (f₂ : G →* G₁)
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)) (g : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u3} N₁ (SemidirectProduct.left.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁ (coeFn.{max (succ (max u3 u4)) (succ (max u1 u2)), max (succ (max u1 u2)) (succ (max u3 u4))} (MonoidHom.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (fun (_x : MonoidHom.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)) (MonoidHom.hasCoeToFun.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (coeFn.{max (succ u3) (succ u1), max (succ u1) (succ u3)} (MonoidHom.{u1, 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 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u2}} {G₁ : Type.{u1}} [_inst_4 : Group.{u2} N₁] [_inst_5 : Group.{u1} G₁] {φ₁ : MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u2)} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u2} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) 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(SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u2, u1} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))) (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))))) f₁ (SemidirectProduct.left.{u4, u3} N G _inst_1 _inst_2 φ g))
+  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u2}} {G₁ : Type.{u1}} [_inst_4 : Group.{u2} N₁] [_inst_5 : Group.{u1} G₁] {φ₁ : MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u2)} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u2} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) 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(SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u3, max u2 u1} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{max u4 u3, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u2, u1} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))) (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))))) f₁ (SemidirectProduct.left.{u4, u3} N G _inst_1 _inst_2 φ g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_left SemidirectProduct.map_leftₓ'. -/
 @[simp]
 theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
@@ -516,7 +516,7 @@ theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)) (g : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u4} G₁ (SemidirectProduct.right.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁ (coeFn.{max (succ (max u3 u4)) (succ (max u1 u2)), max (succ (max u1 u2)) (succ (max u3 u4))} (MonoidHom.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (fun (_x : MonoidHom.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)) (MonoidHom.hasCoeToFun.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, 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 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N 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(SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u1) u2, max u4 u3, max u1 u2} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} 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(SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ (SemidirectProduct.right.{u4, u3} N G _inst_1 _inst_2 φ g))
+  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N 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(MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G 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(SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{max u4 u3, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ (SemidirectProduct.right.{u4, u3} N G _inst_1 _inst_2 φ g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_right SemidirectProduct.map_rightₓ'. -/
 @[simp]
 theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :=
@@ -527,7 +527,7 @@ theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)), Eq.{max (succ u4) (succ (max u1 u2))} (MonoidHom.{max u1 u2, u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G₁ (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHom.comp.{max u1 u2, max u3 u4, u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) G₁ (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (SemidirectProduct.rightHom.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h)) (MonoidHom.comp.{max u1 u2, u2, u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G G₁ (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) f₂ (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u1, u1} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) 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(Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₁) => MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{max u3 u4, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHom.comp.{max u3 u4, max u2 u1, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (SemidirectProduct.rightHom.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h)) (MonoidHom.comp.{max u3 u4, u3, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) f₂ (SemidirectProduct.rightHom.{u4, u3} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u1, u1} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u1, u1} N₁ N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ 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(DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{max u3 u4, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHom.comp.{max u3 u4, max u2 u1, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (SemidirectProduct.rightHom.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h)) (MonoidHom.comp.{max u3 u4, u3, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) f₂ (SemidirectProduct.rightHom.{u4, u3} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_comp_map SemidirectProduct.rightHom_comp_mapₓ'. -/
 @[simp]
 theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom :=
@@ -538,7 +538,7 @@ theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u2) (succ u4)} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHom.comp.{u2, u2, u4} N N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u4, u4} N N₁ N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) 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_inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))))) f₁ n))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u2) (succ u4)} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHom.comp.{u2, u2, u4} N N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u4, u4} N N₁ N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (succ u3) (succ u4), succ u4, max (succ u3) (succ u4)} (MonoidHom.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) => SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) _x) (MulHomClass.toFunLike.{max u3 u4, u4, max u3 u4} (MonoidHom.{u4, max u3 u4} ((fun 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N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max u3 u4, u4, max u3 u4} (MonoidHom.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.inl.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N) => N₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))))) f₁ n))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_inl SemidirectProduct.map_inlₓ'. -/
 @[simp]
 theorem map_inl (n : N) : map f₁ f₂ h (inl n) = inl (f₁ n) := by simp [map]
@@ -548,7 +548,7 @@ theorem map_inl (n : N) : map f₁ f₂ h (inl n) = inl (f₁ n) := by simp [map
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) 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(DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u1, u3, max u3 u4} N N₁ (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inl.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) f₁)
 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u1}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u3)} (MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u3} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u1, u1, u4} (MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u1, u1, u4} (MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ 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(MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} N (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u4 u1, max u3 u2} N (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u4, u1, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inl.{u4, u1} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u3, max u2 u3} N N₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inl.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₁)
+  forall {N : Type.{u4}} {G : Type.{u1}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u3)} (MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u3} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u1, u1, u4} (MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u1, u1, u4} (MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G 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G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} N (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u4 u1, max u3 u2} N (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u4, u1, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inl.{u4, u1} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u3, max u2 u3} N N₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inl.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₁)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_comp_inl SemidirectProduct.map_comp_inlₓ'. -/
 @[simp]
 theorem map_comp_inl : (map f₁ f₂ h).comp inl = inl.comp f₁ := by ext <;> simp
@@ -558,7 +558,7 @@ theorem map_comp_inl : (map f₁ f₂ h).comp inl = inl.comp f₁ := by ext <;>
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} 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 but is expected to have type
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(Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_5)))) (MulOneClass.toMul.{max u3 u4} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_5))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{u3, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_5))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.inr.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) g) _inst_4 _inst_5 φ₁) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} G₁ (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))))) f₂ g))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u2) (succ u4)} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHom.comp.{u2, u2, u4} N N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_5)))) (MulOneClass.toMul.{max u3 u4} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max u3 u4, u3, max u3 u4} (MonoidHom.{u3, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_5))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_5))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{u3, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_5))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.inr.{u4, u3} N₁ ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) g) _inst_4 _inst_5 φ₁) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} G₁ (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))))) f₂ g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_inr SemidirectProduct.map_inrₓ'. -/
 @[simp]
 theorem map_inr (g : G) : map f₁ f₂ h (inr g) = inr (f₂ g) := by simp [map]
@@ -568,7 +568,7 @@ theorem map_inr (g : G) : map f₁ f₂ h (inr g) = inr (f₂ g) := by simp [map
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ 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(MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) 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(DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u2, u4, max u3 u4} G G₁ (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
 but is expected to have type
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(Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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G₁ _inst_5))) (MonoidHom.monoidHomClass.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} G (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u1 u4, max u3 u2} G (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) 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(SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
+  forall {N : Type.{u1}} {G : Type.{u4}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u4} G] {φ : MonoidHom.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u4), succ u4, succ u1} (MonoidHom.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u1 u4, u4, u1} (MonoidHom.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u4} G (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u4, u4, u1} (MonoidHom.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G₁) => MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : G) => G₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u4} G (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} G (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u1 u4, max u3 u2} G (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u4, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inr.{u1, u4} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u2, max u3 u2} G G₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_comp_inr SemidirectProduct.map_comp_inrₓ'. -/
 @[simp]
 theorem map_comp_inr : (map f₁ f₂ h).comp inr = inr.comp f₂ := by ext <;> simp [map]

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

@@ -104,7 +104,7 @@ theorem one_right : (1 : N ⋊[φ] G).right = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (a : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (Inv.inv.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toHasInv.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))) a)) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ (Inv.inv.{u2} G (DivInvMonoid.toHasInv.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u1} N (DivInvMonoid.toHasInv.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ a)))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (Inv.inv.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instInvSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) a)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u2} N (InvOneClass.toInv.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1)))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a)))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (Inv.inv.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instInvSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) a)) (FunLike.coe.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u2} N (InvOneClass.toInv.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1)))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inv_left SemidirectProduct.inv_leftₓ'. -/
 @[simp]
 theorem inv_left (a : N ⋊[φ] G) : a⁻¹.left = φ a.right⁻¹ a.left⁻¹ :=
@@ -126,7 +126,7 @@ theorem inv_right (a : N ⋊[φ] G) : a⁻¹.right = a.right⁻¹ :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (a : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) a b)) (HMul.hMul.{u1, u1, u1} N N N (instHMul.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ a) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ b)))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) a b)) (HMul.hMul.{u2, u2, u2} N ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)) N (instHMul.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) a b)) (HMul.hMul.{u2, u2, u2} N ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)) N (instHMul.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a) (FunLike.coe.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} (MulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.mul_left SemidirectProduct.mul_leftₓ'. -/
 @[simp]
 theorem mul_left (a b : N ⋊[φ] G) : (a * b).left = a.left * φ a.right b.left :=
@@ -260,7 +260,7 @@ theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ =
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut SemidirectProduct.inl_autₓ'. -/
 theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n * inr g⁻¹ := by
   ext <;> simp
@@ -270,7 +270,7 @@ theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n *
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Inv.inv.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toHasInv.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) (Inv.inv.{u2} G (DivInvMonoid.toHasInv.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) g)) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G 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_inst_2 φ) g))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) => SemidirectProduct.{u2, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) G _inst_1 _inst_2 φ) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N (fun (a : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) a) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (InvOneClass.toInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (DivInvOneMonoid.toInvOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (DivisionMonoid.toDivInvOneMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (Group.toDivisionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => 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(MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (a : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) a) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N 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(DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g)) n)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) (SemidirectProduct.{u2, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) 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(MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (InvOneClass.toInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (DivInvOneMonoid.toInvOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) 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(SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} 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 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut_inv SemidirectProduct.inl_aut_invₓ'. -/
 theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr g⁻¹ * inl n * inr g := by
   rw [← MonoidHom.map_inv, inl_aut, inv_inv]
@@ -449,7 +449,7 @@ theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (F : MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), Eq.{max (succ u3) (succ (max u1 u2))} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) F (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u2, max u1 u2, u3} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) (fun (_x : G) => MonoidHom.ext.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) _x)))))) trivial)))
 but is expected to have type
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(Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (MonoidHom.{u2, max u3 u2} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) 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(DivisionMonoid.toDivInvMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3)))) (MonoidHom.monoidHomClass.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))))) F (FunLike.coe.{succ (max u2 u3), succ u3, succ (max u2 u3)} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, 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_inst_2)))) (MulOneClass.toMul.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u3, max u2 u3} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHom.monoidHomClass.{u3, max u2 u3} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u3} N G _inst_1 _inst_2 φ) _x)))))))))
+  forall {N : Type.{u2}} {G : Type.{u3}} {H : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u3} G] [_inst_3 : Group.{u1} H] {φ : MonoidHom.{u3, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (F : MonoidHom.{max u3 u2, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))), Eq.{max (max (succ u2) (succ u3)) (succ u1)} (MonoidHom.{max u3 u2, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) F (SemidirectProduct.lift.{u2, u3, u1} N G H _inst_1 _inst_2 _inst_3 φ (MonoidHom.comp.{u2, max u2 u3, u1} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3))) F (SemidirectProduct.inl.{u2, u3} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u3, max u2 u3, u1} G (SemidirectProduct.{u2, 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_inst_2)))) (MulOneClass.toMul.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u3, max u2 u3} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHom.monoidHomClass.{u3, max u2 u3} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u3} N G _inst_1 _inst_2 φ) _x)))))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_unique SemidirectProduct.lift_uniqueₓ'. -/
 theorem lift_unique (F : N ⋊[φ] G →* H) :
     F = lift (F.comp inl) (F.comp inr) fun _ => by ext <;> simp [inl_aut] :=

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

@@ -104,7 +104,7 @@ theorem one_right : (1 : N ⋊[φ] G).right = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (a : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (Inv.inv.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toHasInv.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))) a)) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ (Inv.inv.{u2} G (DivInvMonoid.toHasInv.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u1} N (DivInvMonoid.toHasInv.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ a)))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (Inv.inv.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instInvSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) a)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u2} N (InvOneClass.toInv.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1)))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a)))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (Inv.inv.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instInvSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) a)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u2} N (InvOneClass.toInv.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1)))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inv_left SemidirectProduct.inv_leftₓ'. -/
 @[simp]
 theorem inv_left (a : N ⋊[φ] G) : a⁻¹.left = φ a.right⁻¹ a.left⁻¹ :=
@@ -126,7 +126,7 @@ theorem inv_right (a : N ⋊[φ] G) : a⁻¹.right = a.right⁻¹ :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (a : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) a b)) (HMul.hMul.{u1, u1, u1} N N N (instHMul.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ a) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ b)))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) a b)) (HMul.hMul.{u2, u2, u2} N ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)) N (instHMul.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) a b)) (HMul.hMul.{u2, u2, u2} N ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)) N (instHMul.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.mul_left SemidirectProduct.mul_leftₓ'. -/
 @[simp]
 theorem mul_left (a b : N ⋊[φ] G) : (a * b).left = a.left * φ a.right b.left :=
@@ -161,7 +161,7 @@ def inl : N →* N ⋊[φ] G where
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) n
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (n : N), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) n
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (n : N), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) n
 Case conversion may be inaccurate. Consider using '#align semidirect_product.left_inl SemidirectProduct.left_inlₓ'. -/
 @[simp]
 theorem left_inl (n : N) : (inl n : N ⋊[φ] G).left = n :=
@@ -172,7 +172,7 @@ theorem left_inl (n : N) : (inl n : N ⋊[φ] G).left = n :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (One.toOfNat1.{u2} G (InvOneClass.toOne.{u2} G (DivInvOneMonoid.toInvOneClass.{u2} G (DivisionMonoid.toDivInvOneMonoid.{u2} G (Group.toDivisionMonoid.{u2} G _inst_2))))))
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (One.toOfNat1.{u2} G (InvOneClass.toOne.{u2} G (DivInvOneMonoid.toInvOneClass.{u2} G (DivisionMonoid.toDivInvOneMonoid.{u2} G (Group.toDivisionMonoid.{u2} G _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_inl SemidirectProduct.right_inlₓ'. -/
 @[simp]
 theorem right_inl (n : N) : (inl n : N ⋊[φ] G).right = 1 :=
@@ -183,7 +183,7 @@ theorem right_inl (n : N) : (inl n : N ⋊[φ] G).right = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u1, max (succ u1) (succ u2)} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u2) (succ u1)} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u2) (succ u1)} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_injective SemidirectProduct.inl_injectiveₓ'. -/
 theorem inl_injective : Function.Injective (inl : N → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨left, left_inl⟩
@@ -193,7 +193,7 @@ theorem inl_injective : Function.Injective (inl : N → N ⋊[φ] G) :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {n₁ : N} {n₂ : N}, Iff (Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n₁) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n₂)) (Eq.{succ u1} N n₁ n₂)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {n₁ : N} {n₂ : N}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₂)) (Eq.{succ u2} N n₁ n₂)
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {n₁ : N} {n₂ : N}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₂)) (Eq.{succ u2} N n₁ n₂)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_inj SemidirectProduct.inl_injₓ'. -/
 @[simp]
 theorem inl_inj {n₁ n₂ : N} : (inl n₁ : N ⋊[φ] G) = inl n₂ ↔ n₁ = n₂ :=
@@ -217,7 +217,7 @@ def inr : G →* N ⋊[φ] G where
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) (OfNat.ofNat.{u1} N 1 (OfNat.mk.{u1} N 1 (One.one.{u1} N (MulOneClass.toHasOne.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (InvOneClass.toOne.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1))))))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (InvOneClass.toOne.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.left_inr SemidirectProduct.left_inrₓ'. -/
 @[simp]
 theorem left_inr (g : G) : (inr g : N ⋊[φ] G).left = 1 :=
@@ -228,7 +228,7 @@ theorem left_inr (g : G) : (inr g : N ⋊[φ] G).left = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_inr SemidirectProduct.right_inrₓ'. -/
 @[simp]
 theorem right_inr (g : G) : (inr g : N ⋊[φ] G).right = g :=
@@ -239,7 +239,7 @@ theorem right_inr (g : G) : (inr g : N ⋊[φ] G).right = g :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u1) (succ u2)} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u1) (succ u2)} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u1) (succ u2)} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inr_injective SemidirectProduct.inr_injectiveₓ'. -/
 theorem inr_injective : Function.Injective (inr : G → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨right, right_inr⟩
@@ -249,7 +249,7 @@ theorem inr_injective : Function.Injective (inr : G → N ⋊[φ] G) :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {g₁ : G} {g₂ : G}, Iff (Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g₁) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g₂)) (Eq.{succ u2} G g₁ g₂)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {g₁ : G} {g₂ : G}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 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(Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G 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(SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g₂)) (Eq.{succ u1} G g₁ g₂)
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {g₁ : G} {g₂ : G}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g₂)) (Eq.{succ u1} G g₁ g₂)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inr_inj SemidirectProduct.inr_injₓ'. -/
 @[simp]
 theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ = g₂ :=
@@ -260,7 +260,7 @@ theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ =
 lean 3 declaration is
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 but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) 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: G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) a) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N 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(Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) 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_inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G 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(SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut SemidirectProduct.inl_autₓ'. -/
 theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n * inr g⁻¹ := by
   ext <;> simp
@@ -270,7 +270,7 @@ theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n *
 lean 3 declaration is
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 but is expected to have type
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+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N 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(Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (InvOneClass.toInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (DivInvOneMonoid.toInvOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (DivisionMonoid.toDivInvOneMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (Group.toDivisionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => 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(MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g)) n)) (HMul.hMul.{max u2 u1, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) => SemidirectProduct.{u2, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) G _inst_1 _inst_2 φ) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N 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((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) (HMul.hMul.{max u1 u2, max u2 u1, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G 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_inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut_inv SemidirectProduct.inl_aut_invₓ'. -/
 theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr g⁻¹ * inl n * inr g := by
   rw [← MonoidHom.map_inv, inl_aut, inv_inv]
@@ -280,7 +280,7 @@ theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr
 lean 3 declaration is
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(Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.mk.{u1, u2} N G _inst_1 _inst_2 φ n g) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N 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 but is expected to have type
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+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u2) (succ u1)} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.mk.{u2, u1} N G _inst_1 _inst_2 φ n g) (HMul.hMul.{max u2 u1, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.mk_eq_inl_mul_inr SemidirectProduct.mk_eq_inl_mul_inrₓ'. -/
 @[simp]
 theorem mk_eq_inl_mul_inr (g : G) (n : N) : (⟨n, g⟩ : N ⋊[φ] G) = inl n * inr g := by ext <;> simp
@@ -290,7 +290,7 @@ theorem mk_eq_inl_mul_inr (g : G) (n : N) : (⟨n, g⟩ : N ⋊[φ] G) = inl n *
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ (max u1 u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ x)) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ x))) x
 but is expected to have type
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φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ x))) x
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_left_mul_inr_right SemidirectProduct.inl_left_mul_inr_rightₓ'. -/
 @[simp]
 theorem inl_left_mul_inr_right (x : N ⋊[φ] G) : inl x.left * inr x.right = x := by ext <;> simp
@@ -313,7 +313,7 @@ def rightHom : N ⋊[φ] G →* G where
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Eq.{max (succ u1) (succ u2)} ((fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ)) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ)) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Eq.{max (succ u2) (succ u1)} (forall (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ)) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ)
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Eq.{max (succ u2) (succ u1)} (forall (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ)) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_eq_right SemidirectProduct.rightHom_eq_rightₓ'. -/
 @[simp]
 theorem rightHom_eq_right : (rightHom : N ⋊[φ] G → G) = right :=
@@ -345,7 +345,7 @@ theorem rightHom_comp_inr : (rightHom : N ⋊[φ] G →* G).comp inr = MonoidHom
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (a : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 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+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_inl SemidirectProduct.rightHom_inlₓ'. -/
 @[simp]
 theorem rightHom_inl (n : N) : rightHom (inl n : N ⋊[φ] G) = 1 := by simp [right_hom]
@@ -355,7 +355,7 @@ theorem rightHom_inl (n : N) : rightHom (inl n : N ⋊[φ] G) = 1 := by simp [ri
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (a : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (a : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_inr SemidirectProduct.rightHom_inrₓ'. -/
 @[simp]
 theorem rightHom_inr (g : G) : rightHom (inr g : N ⋊[φ] G) = g := by simp [right_hom]
@@ -365,7 +365,7 @@ theorem rightHom_inr (g : G) : rightHom (inr g : N ⋊[φ] G) = g := by simp [ri
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Surjective.{max (succ u1) (succ u2), succ u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Surjective.{max (succ u2) (succ u1), succ u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Surjective.{max (succ u2) (succ u1), succ u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_surjective SemidirectProduct.rightHom_surjectiveₓ'. -/
 theorem rightHom_surjective : Function.Surjective (rightHom : N ⋊[φ] G → G) :=
   Function.surjective_iff_hasRightInverse.2 ⟨inr, rightHom_inr⟩
@@ -391,7 +391,7 @@ variable (f₁ : N →* H) (f₂ : G →* H)
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), (forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} 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(Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)) -> (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))
 but is expected to have type
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(DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (FunLike.coe.{succ u3, succ u3, succ u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) => MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) _x) (MulHomClass.toFunLike.{u3, u3, u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3)))) (MulOneClass.toMul.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) (MonoidHomClass.toMulHomClass.{u3, u3, u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u3, u3} ((fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))
+  forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))) (MonoidHomClass.toMulHomClass.{u3, u3, u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift SemidirectProduct.liftₓ'. -/
 /-- Define a group hom `N ⋊[φ] G →* H`, by defining maps `N →* H` and `G →* H`  -/
 def lift (f₁ : N →* H) (f₂ : G →* H)
@@ -409,7 +409,7 @@ def lift (f₁ : N →* H) (f₂ : G →* H)
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, 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 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N 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(DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₁ n)
+  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) => (fun 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(MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => H) _x) (MulHomClass.toFunLike.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{max u2 u1, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) (SemidirectProduct.lift.{u2, u1, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => H) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N H (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₁ n)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_inl SemidirectProduct.lift_inlₓ'. -/
 @[simp]
 theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
@@ -419,7 +419,7 @@ theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} 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(Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) f₁
 but is expected to have type
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(DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))} (f₁ : MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, u3, u2} N N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u3, u3} N N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u3, u2, u2} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) => MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun 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(Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u3 u1, u2} N (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u3, u1, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inl.{u3, u1} N G _inst_1 _inst_2 φ)) f₁
+  forall {N : Type.{u3}} {G : Type.{u1}} {H : Type.{u2}} [_inst_1 : Group.{u3} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u2} H] {φ : MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))} (f₁ : MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, u3, u2} N N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N 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(Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u3 u1, u2} N (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u3, u1, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inl.{u3, u1} N G _inst_1 _inst_2 φ)) f₁
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_comp_inl SemidirectProduct.lift_comp_inlₓ'. -/
 @[simp]
 theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext <;> simp
@@ -429,7 +429,7 @@ theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext <;> simp
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N H H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} H H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) (MonoidHom.hasCoeToFun.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)) (g : G), Eq.{succ u3} H (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u3)} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> H) (MonoidHom.hasCoeToFun.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N 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(DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 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(MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g)
+  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) => (fun 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(MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => H) _x) (MulHomClass.toFunLike.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} 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(Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{max u2 u1, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) (SemidirectProduct.lift.{u2, u1, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G 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(SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_inr SemidirectProduct.lift_inrₓ'. -/
 @[simp]
 theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
@@ -439,7 +439,7 @@ theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} 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(Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, max u1 u2, u3} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) f₂
 but is expected to have type
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(DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u1) (succ u2)} (MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u1, u1, u2} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u2, u2} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) => MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) _x) (MulHomClass.toFunLike.{u2, u2, u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun 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(Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) (MonoidHomClass.toMulHomClass.{u2, u2, u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u1 u3, u2} G (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u1, u3, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inr.{u1, u3} N G _inst_1 _inst_2 φ)) f₂
+  forall {N : Type.{u1}} {G : Type.{u3}} {H : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u3} G] [_inst_3 : Group.{u2} H] {φ : MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u1) (succ u2)} (MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u1, u1, u2} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => H) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u1 u3, u2} G (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u1, u3, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inr.{u1, u3} N G _inst_1 _inst_2 φ)) f₂
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_comp_inr SemidirectProduct.lift_comp_inrₓ'. -/
 @[simp]
 theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
@@ -449,7 +449,7 @@ theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (F : MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), Eq.{max (succ u3) (succ (max u1 u2))} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) F (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u2, max u1 u2, u3} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) (fun (_x : G) => MonoidHom.ext.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) _x)))))) trivial)))
 but is expected to have type
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(Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (MonoidHom.{u2, max u3 u2} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) 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(DivisionMonoid.toDivInvMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3)))) (MonoidHom.monoidHomClass.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))))) F (FunLike.coe.{succ (max u2 u3), succ u3, succ (max u2 u3)} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, 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_inst_2)))) (MulOneClass.toMul.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u3, max u2 u3} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHom.monoidHomClass.{u3, max u2 u3} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u3} N G _inst_1 _inst_2 φ) _x)))))))))
+  forall {N : Type.{u2}} {G : Type.{u3}} {H : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u3} G] [_inst_3 : Group.{u1} H] {φ : MonoidHom.{u3, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (F : MonoidHom.{max u3 u2, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))), Eq.{max (max (succ u2) (succ u3)) (succ u1)} (MonoidHom.{max u3 u2, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) F (SemidirectProduct.lift.{u2, u3, u1} N G H _inst_1 _inst_2 _inst_3 φ (MonoidHom.comp.{u2, max u2 u3, u1} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3))) F (SemidirectProduct.inl.{u2, u3} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u3, max u2 u3, u1} G (SemidirectProduct.{u2, 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φ) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) N (fun (a : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) a) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N 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_inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3))) (MonoidHom.monoidHomClass.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))))) F (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (MonoidHom.{u2, max u3 u2} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) N (fun (a : N) => SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) 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(Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (MonoidHom.{u2, max u3 u2} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u3 u2} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u3} N G _inst_1 _inst_2 φ) x))) (Inv.inv.{u1} H (InvOneClass.toInv.{u1} H (DivInvOneMonoid.toInvOneClass.{u1} H (DivisionMonoid.toDivInvOneMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3)))) (FunLike.coe.{succ (max (max u2 u3) u1), succ (max u2 u3), succ u1} (MonoidHom.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (fun (a : SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) => H) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u3, u1} (MonoidHom.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (MulOneClass.toMul.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} H (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (DivisionMonoid.toDivInvMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3))))) (MonoidHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u3, u1} (MonoidHom.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (DivisionMonoid.toDivInvMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3)))) (MonoidHom.monoidHomClass.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))))) F (FunLike.coe.{succ (max u2 u3), succ u3, succ (max u2 u3)} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, 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_inst_2)))) (MulOneClass.toMul.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u3, max u2 u3} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHom.monoidHomClass.{u3, max u2 u3} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u3} N G _inst_1 _inst_2 φ) _x)))))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_unique SemidirectProduct.lift_uniqueₓ'. -/
 theorem lift_unique (F : N ⋊[φ] G →* H) :
     F = lift (F.comp inl) (F.comp inr) fun _ => by ext <;> simp [inl_aut] :=
@@ -484,7 +484,7 @@ variable {N₁ : Type _} {G₁ : Type _} [Group N₁] [Group G₁] {φ₁ : G₁
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))), (forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)) -> (MonoidHom.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, max u4 u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₁) => MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u3 u4, u4, u3} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u3 u4, u4, u3} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, max u4 u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map SemidirectProduct.mapₓ'. -/
 /-- Define a map from `N ⋊[φ] G` to `N₁ ⋊[φ₁] G₁` given maps `N →* N₁` and `G →* G₁` that
   satisfy a commutativity condition `∀ n g, f₁ (φ g n) = φ₁ (f₂ g) (f₁ n)`.  -/
@@ -505,7 +505,7 @@ variable (f₁ : N →* N₁) (f₂ : G →* G₁)
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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u4} N₁ G₁ _inst_4 _inst_5 φ₁)) (MonoidHom.hasCoeToFun.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (coeFn.{max (succ u3) (succ u1), max (succ u1) (succ u3)} (MonoidHom.{u1, 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 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u2}} {G₁ : Type.{u1}} [_inst_4 : Group.{u2} N₁] [_inst_5 : Group.{u1} G₁] {φ₁ : MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u2)} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u2} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u2, u2} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u2, u2} N₁ N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ 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(Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))) G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ 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N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u1} G₁ (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u3, u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))))) f₂ g))) f₁)) (g : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ), Eq.{succ u2} N₁ (SemidirectProduct.left.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u3), max (succ u2) (succ u1)} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) 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(SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u3, max u2 u1} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} 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(SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u2, u1} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))) (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))))) f₁ (SemidirectProduct.left.{u4, u3} N G _inst_1 _inst_2 φ g))
+  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u2}} {G₁ : Type.{u1}} [_inst_4 : Group.{u2} N₁] [_inst_5 : Group.{u1} G₁] {φ₁ : MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u2)} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u2} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u2, u2} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u2, u2} N₁ N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ 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(Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))) G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u1} G₁ (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u3, u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))))) f₂ g))) f₁)) (g : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ), Eq.{succ u2} N₁ (SemidirectProduct.left.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u3), max (succ u2) (succ u1)} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) => SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u3, max u2 u1} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u3, max u2 u1} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{max u4 u3, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u2, u1} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))) (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))))) f₁ (SemidirectProduct.left.{u4, u3} N G _inst_1 _inst_2 φ g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_left SemidirectProduct.map_leftₓ'. -/
 @[simp]
 theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
@@ -516,7 +516,7 @@ theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ g))
 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u1, u1} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u1, u1} N₁ N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₁) => MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) 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(MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) 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N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)) (g : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ), Eq.{succ u2} G₁ (SemidirectProduct.right.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), max (succ u4) (succ u3), max (succ u1) (succ u2)} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) 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(SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u1) u2, max u4 u3, max u1 u2} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} 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(SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ (SemidirectProduct.right.{u4, u3} N G _inst_1 _inst_2 φ g))
+  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u1, u1} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u1, u1} N₁ N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ 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(DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)) (g : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ), Eq.{succ u2} G₁ (SemidirectProduct.right.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), max (succ u4) (succ u3), max (succ u1) (succ u2)} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) => SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u1) u2, max u4 u3, max u1 u2} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u1) u2, max u4 u3, max u1 u2} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{max u4 u3, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ (SemidirectProduct.right.{u4, u3} N G _inst_1 _inst_2 φ g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_right SemidirectProduct.map_rightₓ'. -/
 @[simp]
 theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :=
@@ -527,7 +527,7 @@ theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)), Eq.{max (succ u4) (succ (max u1 u2))} (MonoidHom.{max u1 u2, u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G₁ (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHom.comp.{max u1 u2, max u3 u4, u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) G₁ (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (SemidirectProduct.rightHom.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h)) (MonoidHom.comp.{max u1 u2, u2, u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G G₁ (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) f₂ (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N 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(MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N 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(DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u1, u1} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) 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(MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{max u3 u4, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHom.comp.{max u3 u4, max u2 u1, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (SemidirectProduct.rightHom.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h)) (MonoidHom.comp.{max u3 u4, u3, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) f₂ (SemidirectProduct.rightHom.{u4, u3} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G 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G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{max u3 u4, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHom.comp.{max u3 u4, max u2 u1, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (SemidirectProduct.rightHom.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h)) (MonoidHom.comp.{max u3 u4, u3, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) f₂ (SemidirectProduct.rightHom.{u4, u3} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_comp_map SemidirectProduct.rightHom_comp_mapₓ'. -/
 @[simp]
 theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom :=
@@ -538,7 +538,7 @@ theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} 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 but is expected to have type
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(Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ 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: N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) _inst_4)))) (MulOneClass.toMul.{max u3 u4} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max u3 u4, u4, max u3 u4} (MonoidHom.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.inl.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))))) f₁ n))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u2) (succ u4)} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHom.comp.{u2, u2, u4} N N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N 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: N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) _inst_4)))) (MulOneClass.toMul.{max u3 u4} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max u3 u4, u4, max u3 u4} (MonoidHom.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.inl.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N) => N₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))))) f₁ n))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_inl SemidirectProduct.map_inlₓ'. -/
 @[simp]
 theorem map_inl (n : N) : map f₁ f₂ h (inl n) = inl (f₁ n) := by simp [map]
@@ -548,7 +548,7 @@ theorem map_inl (n : N) : map f₁ f₂ h (inl n) = inl (f₁ n) := by simp [map
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ 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(MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) 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(DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u1, u3, max u3 u4} N N₁ (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ 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 but is expected to have type
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(Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u3)} (MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u3} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) 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G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} N (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u4 u1, max u3 u2} N (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) 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(SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inl.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₁)
+  forall {N : Type.{u4}} {G : Type.{u1}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u3)} (MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u3} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N 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(MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u1, u1, u4} (MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G₁) => MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} N (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u4 u1, max u3 u2} N (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u4, u1, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inl.{u4, u1} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u3, max u2 u3} N N₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inl.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₁)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_comp_inl SemidirectProduct.map_comp_inlₓ'. -/
 @[simp]
 theorem map_comp_inl : (map f₁ f₂ h).comp inl = inl.comp f₁ := by ext <;> simp
@@ -558,7 +558,7 @@ theorem map_comp_inl : (map f₁ f₂ h).comp inl = inl.comp f₁ := by ext <;>
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.inr.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u2) (succ u4)} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHom.comp.{u2, u2, u4} N N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N 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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u4, u4} N N₁ N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) 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(Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} G₁ (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))))) f₂ g))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u2) (succ u4)} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHom.comp.{u2, u2, u4} N N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N 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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u4, u4} N N₁ N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) 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(Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} G₁ (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))))) f₂ g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_inr SemidirectProduct.map_inrₓ'. -/
 @[simp]
 theorem map_inr (g : G) : map f₁ f₂ h (inr g) = inr (f₂ g) := by simp [map]
@@ -568,7 +568,7 @@ theorem map_inr (g : G) : map f₁ f₂ h (inr g) = inr (f₂ g) := by simp [map
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N 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(Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)), Eq.{max (succ (max u3 u4)) (succ u2)} (MonoidHom.{u2, max u3 u4} G (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u2, max u1 u2, max u3 u4} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u2, u4, max u3 u4} G G₁ (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u4}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u4} G] {φ : MonoidHom.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u4} G (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N 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(DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₁) => MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} 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(Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u4} G (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} G (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u1 u4, max u3 u2} G (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u4, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inr.{u1, u4} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u2, max u3 u2} G G₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
+  forall {N : Type.{u1}} {G : Type.{u4}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u4} G] {φ : MonoidHom.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) 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(Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : G) => G₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u4} G (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} G (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u1 u4, max u3 u2} G (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u4, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inr.{u1, u4} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u2, max u3 u2} G G₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_comp_inr SemidirectProduct.map_comp_inrₓ'. -/
 @[simp]
 theorem map_comp_inr : (map f₁ f₂ h).comp inr = inr.comp f₂ := by ext <;> simp [map]

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

@@ -104,7 +104,7 @@ theorem one_right : (1 : N ⋊[φ] G).right = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (a : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (Inv.inv.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toHasInv.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))) a)) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ (Inv.inv.{u2} G (DivInvMonoid.toHasInv.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u1} N (DivInvMonoid.toHasInv.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ a)))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (Inv.inv.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instInvSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) a)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} 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(MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u2} N (InvOneClass.toInv.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1)))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a)))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (Inv.inv.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instInvSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) a)) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a))) (Inv.inv.{u2} N (InvOneClass.toInv.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1)))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inv_left SemidirectProduct.inv_leftₓ'. -/
 @[simp]
 theorem inv_left (a : N ⋊[φ] G) : a⁻¹.left = φ a.right⁻¹ a.left⁻¹ :=
@@ -126,7 +126,7 @@ theorem inv_right (a : N ⋊[φ] G) : a⁻¹.right = a.right⁻¹ :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (a : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) a b)) (HMul.hMul.{u1, u1, u1} N N N (instHMul.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ a) (coeFn.{succ u1, succ u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (fun (_x : MulEquiv.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) => N -> N) (MulEquiv.hasCoeToFun.{u1, u1} N N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ b)))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) a b)) (HMul.hMul.{u2, u2, u2} N ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)) N (instHMul.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N 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(MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (b : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (HMul.hMul.{max u2 u1, max u2 u1, max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) a b)) (HMul.hMul.{u2, u2, u2} N ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)) N (instHMul.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ a) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N (fun (_x : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) _x) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ a)) (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ b)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.mul_left SemidirectProduct.mul_leftₓ'. -/
 @[simp]
 theorem mul_left (a b : N ⋊[φ] G) : (a * b).left = a.left * φ a.right b.left :=
@@ -161,7 +161,7 @@ def inl : N →* N ⋊[φ] G where
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) n
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (n : N), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) n
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (n : N), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) n
 Case conversion may be inaccurate. Consider using '#align semidirect_product.left_inl SemidirectProduct.left_inlₓ'. -/
 @[simp]
 theorem left_inl (n : N) : (inl n : N ⋊[φ] G).left = n :=
@@ -172,7 +172,7 @@ theorem left_inl (n : N) : (inl n : N ⋊[φ] G).left = n :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (One.toOfNat1.{u2} G (InvOneClass.toOne.{u2} G (DivInvOneMonoid.toInvOneClass.{u2} G (DivisionMonoid.toDivInvOneMonoid.{u2} G (Group.toDivisionMonoid.{u2} G _inst_2))))))
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (One.toOfNat1.{u2} G (InvOneClass.toOne.{u2} G (DivInvOneMonoid.toInvOneClass.{u2} G (DivisionMonoid.toDivInvOneMonoid.{u2} G (Group.toDivisionMonoid.{u2} G _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_inl SemidirectProduct.right_inlₓ'. -/
 @[simp]
 theorem right_inl (n : N) : (inl n : N ⋊[φ] G).right = 1 :=
@@ -183,7 +183,7 @@ theorem right_inl (n : N) : (inl n : N ⋊[φ] G).right = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u1, max (succ u1) (succ u2)} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u2) (succ u1)} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u2) (succ u1)} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_injective SemidirectProduct.inl_injectiveₓ'. -/
 theorem inl_injective : Function.Injective (inl : N → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨left, left_inl⟩
@@ -193,7 +193,7 @@ theorem inl_injective : Function.Injective (inl : N → N ⋊[φ] G) :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {n₁ : N} {n₂ : N}, Iff (Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n₁) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n₂)) (Eq.{succ u1} N n₁ n₂)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {n₁ : N} {n₂ : N}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₂)) (Eq.{succ u2} N n₁ n₂)
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {n₁ : N} {n₂ : N}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₁) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n₂)) (Eq.{succ u2} N n₁ n₂)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_inj SemidirectProduct.inl_injₓ'. -/
 @[simp]
 theorem inl_inj {n₁ n₂ : N} : (inl n₁ : N ⋊[φ] G) = inl n₂ ↔ n₁ = n₂ :=
@@ -217,7 +217,7 @@ def inr : G →* N ⋊[φ] G where
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u1} N (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) (OfNat.ofNat.{u1} N 1 (OfNat.mk.{u1} N 1 (One.one.{u1} N (MulOneClass.toHasOne.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (InvOneClass.toOne.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1))))))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G), Eq.{succ u2} N (SemidirectProduct.left.{u2, u1} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (OfNat.ofNat.{u2} N 1 (One.toOfNat1.{u2} N (InvOneClass.toOne.{u2} N (DivInvOneMonoid.toInvOneClass.{u2} N (DivisionMonoid.toDivInvOneMonoid.{u2} N (Group.toDivisionMonoid.{u2} N _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.left_inr SemidirectProduct.left_inrₓ'. -/
 @[simp]
 theorem left_inr (g : G) : (inr g : N ⋊[φ] G).left = 1 :=
@@ -228,7 +228,7 @@ theorem left_inr (g : G) : (inr g : N ⋊[φ] G).left = 1 :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_inr SemidirectProduct.right_inrₓ'. -/
 @[simp]
 theorem right_inr (g : G) : (inr g : N ⋊[φ] G).right = g :=
@@ -239,7 +239,7 @@ theorem right_inr (g : G) : (inr g : N ⋊[φ] G).right = g :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u1) (succ u2)} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u1) (succ u2)} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Injective.{succ u2, max (succ u1) (succ u2)} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inr_injective SemidirectProduct.inr_injectiveₓ'. -/
 theorem inr_injective : Function.Injective (inr : G → N ⋊[φ] G) :=
   Function.injective_iff_hasLeftInverse.2 ⟨right, right_inr⟩
@@ -249,7 +249,7 @@ theorem inr_injective : Function.Injective (inr : G → N ⋊[φ] G) :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {g₁ : G} {g₂ : G}, Iff (Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g₁) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g₂)) (Eq.{succ u2} G g₁ g₂)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {g₁ : G} {g₂ : G}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 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(Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G 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(SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g₂)) (Eq.{succ u1} G g₁ g₂)
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {g₁ : G} {g₂ : G}, Iff (Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g₁) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g₂)) (Eq.{succ u1} G g₁ g₂)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inr_inj SemidirectProduct.inr_injₓ'. -/
 @[simp]
 theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ = g₂ :=
@@ -260,7 +260,7 @@ theorem inr_inj {g₁ g₂ : G} : (inr g₁ : N ⋊[φ] G) = inr g₂ ↔ g₁ =
 lean 3 declaration is
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 but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) 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: G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) a) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N 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(Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) 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_inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G 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(SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut SemidirectProduct.inl_autₓ'. -/
 theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n * inr g⁻¹ := by
   ext <;> simp
@@ -270,7 +270,7 @@ theorem inl_aut (g : G) (n : N) : (inl (φ g n) : N ⋊[φ] G) = inr g * inl n *
 lean 3 declaration is
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 but is expected to have type
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+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulEquiv.instMulEquivClassMulEquiv.{u2, u2} N N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (Inv.inv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (InvOneClass.toInv.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (DivInvOneMonoid.toInvOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (DivisionMonoid.toDivInvOneMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) g) (Group.toDivisionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => 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(MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g)) n)) (HMul.hMul.{max u2 u1, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) => SemidirectProduct.{u2, u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) n) G _inst_1 _inst_2 φ) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N 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((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) (HMul.hMul.{max u1 u2, max u2 u1, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G 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_inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (Inv.inv.{u1} G (InvOneClass.toInv.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_2)))) g)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} 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N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_aut_inv SemidirectProduct.inl_aut_invₓ'. -/
 theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr g⁻¹ * inl n * inr g := by
   rw [← MonoidHom.map_inv, inl_aut, inv_inv]
@@ -280,7 +280,7 @@ theorem inl_aut_inv (g : G) (n : N) : (inl ((φ g)⁻¹ n) : N ⋊[φ] G) = inr
 lean 3 declaration is
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(Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u1) (succ u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.mk.{u1, u2} N G _inst_1 _inst_2 φ n g) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N 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 but is expected to have type
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+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (g : G) (n : N), Eq.{max (succ u2) (succ u1)} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.mk.{u2, u1} N G _inst_1 _inst_2 φ n g) (HMul.hMul.{max u2 u1, max u1 u2, max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) g) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (instHMul.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) n) (SemidirectProduct.instMulSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.mk_eq_inl_mul_inr SemidirectProduct.mk_eq_inl_mul_inrₓ'. -/
 @[simp]
 theorem mk_eq_inl_mul_inr (g : G) (n : N) : (⟨n, g⟩ : N ⋊[φ] G) = inl n * inr g := by ext <;> simp
@@ -290,7 +290,7 @@ theorem mk_eq_inl_mul_inr (g : G) (n : N) : (⟨n, g⟩ : N ⋊[φ] G) = inl n *
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ), Eq.{succ (max u1 u2)} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (HMul.hMul.{max u1 u2, max u1 u2, max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (instHMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toHasMul.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))))) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.left.{u1, u2} N G _inst_1 _inst_2 φ x)) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ x))) x
 but is expected to have type
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φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ x))) x
 Case conversion may be inaccurate. Consider using '#align semidirect_product.inl_left_mul_inr_right SemidirectProduct.inl_left_mul_inr_rightₓ'. -/
 @[simp]
 theorem inl_left_mul_inr_right (x : N ⋊[φ] G) : inl x.left * inr x.right = x := by ext <;> simp
@@ -313,7 +313,7 @@ def rightHom : N ⋊[φ] G →* G where
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Eq.{max (succ u1) (succ u2)} ((fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ)) (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ)) (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Eq.{max (succ u2) (succ u1)} (forall (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ)) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ)
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Eq.{max (succ u2) (succ u1)} (forall (a : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) a) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ)) (SemidirectProduct.right.{u2, u1} N G _inst_1 _inst_2 φ)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_eq_right SemidirectProduct.rightHom_eq_rightₓ'. -/
 @[simp]
 theorem rightHom_eq_right : (rightHom : N ⋊[φ] G → G) = right :=
@@ -345,7 +345,7 @@ theorem rightHom_comp_inr : (rightHom : N ⋊[φ] G →* G).comp inr = MonoidHom
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} G (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u1), max (succ u1) (succ (max u1 u2))} (MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => N -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u1, max u1 u2} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (OfNat.ofNat.{u2} G 1 (OfNat.mk.{u2} G 1 (One.one.{u2} G (MulOneClass.toHasOne.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (n : N), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (fun (a : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (MonoidHom.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u2 u1} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 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+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ) n)) _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_inl SemidirectProduct.rightHom_inlₓ'. -/
 @[simp]
 theorem rightHom_inl (n : N) : rightHom (inl n : N ⋊[φ] G) = 1 := by simp [right_hom]
@@ -355,7 +355,7 @@ theorem rightHom_inl (n : N) : rightHom (inl n : N ⋊[φ] G) = 1 := by simp [ri
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} G (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (a : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} 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(Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (g : G), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (a : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) a) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (MonoidHom.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u2 u1} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) g
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_inr SemidirectProduct.rightHom_inrₓ'. -/
 @[simp]
 theorem rightHom_inr (g : G) : rightHom (inr g : N ⋊[φ] G) = g := by simp [right_hom]
@@ -365,7 +365,7 @@ theorem rightHom_inr (g : G) : rightHom (inr g : N ⋊[φ] G) = g := by simp [ri
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))}, Function.Surjective.{max (succ u1) (succ u2), succ u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (coeFn.{max (succ u2) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u2)} (MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (fun (_x : MonoidHom.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> G) (MonoidHom.hasCoeToFun.{max u1 u2, u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Surjective.{max (succ u2) (succ u1), succ u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))}, Function.Surjective.{max (succ u2) (succ u1), succ u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) G (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))))) (SemidirectProduct.rightHom.{u2, u1} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_surjective SemidirectProduct.rightHom_surjectiveₓ'. -/
 theorem rightHom_surjective : Function.Surjective (rightHom : N ⋊[φ] G → G) :=
   Function.surjective_iff_hasRightInverse.2 ⟨inr, rightHom_inr⟩
@@ -391,7 +391,7 @@ variable (f₁ : N →* H) (f₂ : G →* H)
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), (forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} 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(Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)) -> (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))
 but is expected to have type
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(DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (FunLike.coe.{succ u3, succ u3, succ u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) => MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) _x) (MulHomClass.toFunLike.{u3, u3, u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3)))) (MulOneClass.toMul.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))))))) (MonoidHomClass.toMulHomClass.{u3, u3, u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) 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_inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u3, u3} ((fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))
+  forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) (MonoidHomClass.toMulHomClass.{u3, u3, u3} (MonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift SemidirectProduct.liftₓ'. -/
 /-- Define a group hom `N ⋊[φ] G →* H`, by defining maps `N →* H` and `G →* H`  -/
 def lift (f₁ : N →* H) (f₂ : G →* H)
@@ -409,7 +409,7 @@ def lift (f₁ : N →* H) (f₂ : G →* H)
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, 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 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) 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(DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₁ n)
+  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) => (fun 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(MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => H) _x) (MulHomClass.toFunLike.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{max u2 u1, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) (SemidirectProduct.lift.{u2, u1, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) _x) (MulHomClass.toFunLike.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, max u1 u2} (MonoidHom.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u1 u2} N (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u1} N G _inst_1 _inst_2 φ) n)) (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => H) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N H (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u2 u3, u2, u3} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₁ n)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_inl SemidirectProduct.lift_inlₓ'. -/
 @[simp]
 theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
@@ -419,7 +419,7 @@ theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} 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(Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) f₁
 but is expected to have type
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(DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))} (f₁ : MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, u3, u2} N N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u3, u3} N N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))) G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N 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H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun 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G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u3 u1, u2} N (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u3, u1, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inl.{u3, u1} N G _inst_1 _inst_2 φ)) f₁
+  forall {N : Type.{u3}} {G : Type.{u1}} {H : Type.{u2}} [_inst_1 : Group.{u3} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u2} H] {φ : MonoidHom.{u1, u3} G (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))) (MulAut.instGroupMulAut.{u3} N (MulOneClass.toMul.{u3} N (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))))))))} (f₁ : MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, u3, u2} N N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N 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(Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u2} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} N H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u3 u1, u2} N (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} N (DivInvMonoid.toMonoid.{u3} N (Group.toDivInvMonoid.{u3} N _inst_1))) (Monoid.toMulOneClass.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u3 u1} (SemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u3, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u3, u1, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inl.{u3, u1} N G _inst_1 _inst_2 φ)) f₁
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_comp_inl SemidirectProduct.lift_comp_inlₓ'. -/
 @[simp]
 theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext <;> simp
@@ -429,7 +429,7 @@ theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext <;> simp
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N H H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} H H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) (MonoidHom.hasCoeToFun.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)) (g : G), Eq.{succ u3} H (coeFn.{max (succ u3) (succ (max u1 u2)), max (succ (max u1 u2)) (succ u3)} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) -> H) (MonoidHom.hasCoeToFun.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (coeFn.{max (succ (max u1 u2)) (succ u2), max (succ u2) (succ (max u1 u2))} (MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (fun (_x : MonoidHom.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) => G -> (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.hasCoeToFun.{u2, max u1 u2} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) g)) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g)
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N 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_inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) 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(MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g)
+  forall {N : Type.{u2}} {G : Type.{u1}} {H : Type.{u3}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (f₁ : MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u2) (succ u3)} (MonoidHom.{u2, u3} N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, u2, u3} N N H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u3, u3} N ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u3, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) => (fun 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(MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, max u1 u2} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) => H) _x) (MulHomClass.toFunLike.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} 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(Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max (max u2 u1) u3, max u2 u1, u3} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{max u2 u1, u3} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) (SemidirectProduct.lift.{u2, u1, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (MonoidHom.{u1, max u1 u2} G (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u1} G 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(SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u1} N G _inst_1 _inst_2 φ) g)) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.monoidHomClass.{u1, u3} G H (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))))) f₂ g)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_inr SemidirectProduct.lift_inrₓ'. -/
 @[simp]
 theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
@@ -439,7 +439,7 @@ theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (f₂ : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} 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_inst_3))) (coeFn.{succ u3, succ u3} (MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) (fun (_x : MonoidHom.{u3, u3} H (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))) (MulAut.group.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))))))))) => H -> (MulAut.{u3} H (MulOneClass.toHasMul.{u3} H (Monoid.toMulOneClass.{u3} 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(Group.toDivInvMonoid.{u3} H _inst_3))))))))) (MulAut.conj.{u3} H _inst_3) (coeFn.{max (succ u3) (succ u2), max (succ u2) (succ u3)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (fun (_x : MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) => G -> H) (MonoidHom.hasCoeToFun.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u2, u3} G H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) (MonoidHom.comp.{u2, max u1 u2, u3} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) f₂
 but is expected to have type
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(DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u1) (succ u2)} (MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u1, u1, u2} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N 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: G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (MulEquiv.toMonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (FunLike.coe.{succ u2, succ u2, succ u2} (MonoidHom.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun 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G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun 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(Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => H) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u1 u3, u2} G (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u1, u3, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inr.{u1, u3} N G _inst_1 _inst_2 φ)) f₂
+  forall {N : Type.{u1}} {G : Type.{u3}} {H : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u3} G] [_inst_3 : Group.{u2} H] {φ : MonoidHom.{u3, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (f₁ : MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (f₂ : MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (h : forall (g : G), Eq.{max (succ u1) (succ u2)} (MonoidHom.{u1, u2} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u1, u1, u2} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N 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(Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun 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_inst_3))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3)))))))) (MonoidHom.monoidHomClass.{u2, u2} ((fun 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(DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))) (MulAut.instGroupMulAut.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3))))))))))) (MulAut.conj.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) g) _inst_3) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => H) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} H (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (MonoidHom.monoidHomClass.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))))) f₂ g))) f₁)), Eq.{max (succ u3) (succ u2)} (MonoidHom.{u3, u2} G H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3)))) (MonoidHom.comp.{u3, max u1 u3, u2} G (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u3} (SemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} H (DivInvMonoid.toMonoid.{u2} H (Group.toDivInvMonoid.{u2} H _inst_3))) (SemidirectProduct.lift.{u1, u3, u2} N G H _inst_1 _inst_2 _inst_3 φ f₁ f₂ h) (SemidirectProduct.inr.{u1, u3} N G _inst_1 _inst_2 φ)) f₂
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_comp_inr SemidirectProduct.lift_comp_inrₓ'. -/
 @[simp]
 theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
@@ -449,7 +449,7 @@ theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext <;> simp
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} {H : Type.{u3}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] [_inst_3 : Group.{u3} H] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} (F : MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))), Eq.{max (succ u3) (succ (max u1 u2))} (MonoidHom.{max u1 u2, u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3)))) F (SemidirectProduct.lift.{u1, u2, u3} N G H _inst_1 _inst_2 _inst_3 φ (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u2, max u1 u2, u3} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) (fun (_x : G) => MonoidHom.ext.{u1, u3} N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.comp.{u1, u1, u3} N N H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) (MonoidHom.comp.{u1, max u1 u2, u3} N (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} H (DivInvMonoid.toMonoid.{u3} H (Group.toDivInvMonoid.{u3} H _inst_3))) F (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ))))) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ) _x)))))) trivial)))
 but is expected to have type
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(Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (MonoidHom.{u2, max u3 u2} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) 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(DivisionMonoid.toDivInvMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3)))) (MonoidHom.monoidHomClass.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))))) F (FunLike.coe.{succ (max u2 u3), succ u3, succ (max u2 u3)} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, 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_inst_2)))) (MulOneClass.toMul.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u3, max u2 u3} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHom.monoidHomClass.{u3, max u2 u3} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u3} N G _inst_1 _inst_2 φ) _x)))))))))
+  forall {N : Type.{u2}} {G : Type.{u3}} {H : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u3} G] [_inst_3 : Group.{u1} H] {φ : MonoidHom.{u3, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} (F : MonoidHom.{max u3 u2, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))), Eq.{max (max (succ u2) (succ u3)) (succ u1)} (MonoidHom.{max u3 u2, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) F (SemidirectProduct.lift.{u2, u3, u1} N G H _inst_1 _inst_2 _inst_3 φ (MonoidHom.comp.{u2, max u2 u3, u1} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3))) F (SemidirectProduct.inl.{u2, u3} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u3, max u2 u3, u1} G (SemidirectProduct.{u2, 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φ) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) N (fun (a : N) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : N) => N) a) (EmbeddingLike.toFunLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) N N (EquivLike.toEmbeddingLike.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) N N (MulEquivClass.toEquivLike.{u2, u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N 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_inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3))) (MonoidHom.monoidHomClass.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))))) F (FunLike.coe.{max (succ u3) (succ u2), succ u2, max (succ u3) (succ u2)} (MonoidHom.{u2, max u3 u2} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) N (fun (a : N) => SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) 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(Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, max u3 u2} (MonoidHom.{u2, max u3 u2} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (MonoidHom.monoidHomClass.{u2, max u3 u2} N (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inl.{u2, u3} N G _inst_1 _inst_2 φ) x))) (Inv.inv.{u1} H (InvOneClass.toInv.{u1} H (DivInvOneMonoid.toInvOneClass.{u1} H (DivisionMonoid.toDivInvOneMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3)))) (FunLike.coe.{succ (max (max u2 u3) u1), succ (max u2 u3), succ u1} (MonoidHom.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (fun (a : SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) => H) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u3, u1} (MonoidHom.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (MulOneClass.toMul.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{u1} H (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (DivisionMonoid.toDivInvMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3))))) (MonoidHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u3, u1} (MonoidHom.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))) (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (DivisionMonoid.toDivInvMonoid.{u1} H (Group.toDivisionMonoid.{u1} H _inst_3)))) (MonoidHom.monoidHomClass.{max u2 u3, u1} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) H (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u1} H (DivInvMonoid.toMonoid.{u1} H (Group.toDivInvMonoid.{u1} H _inst_3)))))) F (FunLike.coe.{succ (max u2 u3), succ u3, succ (max u2 u3)} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, 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_inst_2)))) (MulOneClass.toMul.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ)))))) (MonoidHomClass.toMulHomClass.{max u2 u3, u3, max u2 u3} (MonoidHom.{u3, max u3 u2} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivisionMonoid.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivisionMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))) (MonoidHom.monoidHomClass.{u3, max u2 u3} G (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u2 u3} (SemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u2, u3} N G _inst_1 _inst_2 φ))))))) (SemidirectProduct.inr.{u2, u3} N G _inst_1 _inst_2 φ) _x)))))))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.lift_unique SemidirectProduct.lift_uniqueₓ'. -/
 theorem lift_unique (F : N ⋊[φ] G →* H) :
     F = lift (F.comp inl) (F.comp inr) fun _ => by ext <;> simp [inl_aut] :=
@@ -484,7 +484,7 @@ variable {N₁ : Type _} {G₁ : Type _} [Group N₁] [Group G₁] {φ₁ : G₁
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))), (forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)) -> (MonoidHom.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => G₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, max u4 u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
+  forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))), (forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u2, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (FunLike.coe.{max (succ u3) (succ u4), succ u4, succ u3} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₁) => MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u3 u4, u4, u3} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u3 u4, u4, u3} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2)))) (MulOneClass.toMul.{u4} G₁ (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))))) f₂ g))) f₁)) -> (MonoidHom.{max u2 u1, max u4 u3} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map SemidirectProduct.mapₓ'. -/
 /-- Define a map from `N ⋊[φ] G` to `N₁ ⋊[φ₁] G₁` given maps `N →* N₁` and `G →* G₁` that
   satisfy a commutativity condition `∀ n g, f₁ (φ g n) = φ₁ (f₂ g) (f₁ n)`.  -/
@@ -505,7 +505,7 @@ variable (f₁ : N →* N₁) (f₂ : G →* G₁)
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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u4} N₁ G₁ _inst_4 _inst_5 φ₁)) (MonoidHom.hasCoeToFun.{max u1 u2, max u3 u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (coeFn.{max (succ u3) (succ u1), max (succ u1) (succ u3)} (MonoidHom.{u1, 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 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u2}} {G₁ : Type.{u1}} [_inst_4 : Group.{u2} N₁] [_inst_5 : Group.{u1} G₁] {φ₁ : MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u2)} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u2} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u2, u2} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u2, u2} N₁ N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ 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(Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))) G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ 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N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u1} G₁ (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u3, u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))))) f₂ g))) f₁)) (g : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ), Eq.{succ u2} N₁ (SemidirectProduct.left.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u3), max (succ u2) (succ u1)} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) 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_inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u3, max u2 u1} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} 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(SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u2, u1} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))) (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))))) f₁ (SemidirectProduct.left.{u4, u3} N G _inst_1 _inst_2 φ g))
+  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u2}} {G₁ : Type.{u1}} [_inst_4 : Group.{u2} N₁] [_inst_5 : Group.{u1} G₁] {φ₁ : MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u2)} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u2} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u2, u2} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u2, u2} N₁ N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ 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(MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))) G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u1, u2} G₁ (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u2} N₁ (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u1), succ u3, succ u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u1, u3, u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u1} G₁ (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u3, u1} (MonoidHom.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u1} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u1} G₁ (DivInvMonoid.toMonoid.{u1} G₁ (Group.toDivInvMonoid.{u1} G₁ _inst_5)))))) f₂ g))) f₁)) (g : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ), Eq.{succ u2} N₁ (SemidirectProduct.left.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u2)) (succ u1), max (succ u4) (succ u3), max (succ u2) (succ u1)} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) => SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u2) u1, max u4 u3, max u2 u1} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u2) u1, max u4 u3, max u2 u1} (MonoidHom.{max u3 u4, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{max u4 u3, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u2 u1} (SemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u2, u1} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u2, u1} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))) (MulOneClass.toMul.{u2} N₁ (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u4, u2} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u2} N₁ (DivInvMonoid.toMonoid.{u2} N₁ (Group.toDivInvMonoid.{u2} N₁ _inst_4)))))) f₁ (SemidirectProduct.left.{u4, u3} N G _inst_1 _inst_2 φ g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_left SemidirectProduct.map_leftₓ'. -/
 @[simp]
 theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
@@ -516,7 +516,7 @@ theorem map_left (g : N ⋊[φ] G) : (map f₁ f₂ h g).left = f₁ g.left :=
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ (SemidirectProduct.right.{u1, u2} N G _inst_1 _inst_2 φ g))
 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u1, u1} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u1, u1} N₁ N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₁) => MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) 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(MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) 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N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)) (g : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ), Eq.{succ u2} G₁ (SemidirectProduct.right.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), max (succ u4) (succ u3), max (succ u1) (succ u2)} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) 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(SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u1) u2, max u4 u3, max u1 u2} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} 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(SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ (SemidirectProduct.right.{u4, u3} N G _inst_1 _inst_2 φ g))
+  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u1, u1} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u1, u1} N₁ N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ 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(DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)) (g : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ), Eq.{succ u2} G₁ (SemidirectProduct.right.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁ (FunLike.coe.{max (max (max (succ u4) (succ u3)) (succ u1)) (succ u2), max (succ u4) (succ u3), max (succ u1) (succ u2)} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (fun (_x : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) => SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) _x) (MulHomClass.toFunLike.{max (max (max u4 u3) u1) u2, max u4 u3, max u1 u2} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ))))) (MulOneClass.toMul.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max (max (max u4 u3) u1) u2, max u4 u3, max u1 u2} (MonoidHom.{max u3 u4, max u2 u1} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{max u4 u3, max u1 u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) g)) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ (SemidirectProduct.right.{u4, u3} N G _inst_1 _inst_2 φ g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_right SemidirectProduct.map_rightₓ'. -/
 @[simp]
 theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :=
@@ -527,7 +527,7 @@ theorem map_right (g : N ⋊[φ] G) : (map f₁ f₂ h g).right = f₂ g.right :
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)), Eq.{max (succ u4) (succ (max u1 u2))} (MonoidHom.{max u1 u2, u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G₁ (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (MonoidHom.comp.{max u1 u2, max u3 u4, u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) G₁ (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (SemidirectProduct.rightHom.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h)) (MonoidHom.comp.{max u1 u2, u2, u4} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) G G₁ (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) f₂ (SemidirectProduct.rightHom.{u1, u2} N G _inst_1 _inst_2 φ))
 but is expected to have type
-  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N 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(MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N 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(DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u1, u1} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) 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(MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))) G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => G₁) _x) (MulHomClass.toFunLike.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u3 u2, u3, u2} (MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{max u3 u4, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHom.comp.{max u3 u4, max u2 u1, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (SemidirectProduct.rightHom.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h)) (MonoidHom.comp.{max u3 u4, u3, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) f₂ (SemidirectProduct.rightHom.{u4, u3} N G _inst_1 _inst_2 φ))
+  forall {N : Type.{u4}} {G : Type.{u3}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u3} G] {φ : MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u1}} {G₁ : Type.{u2}} [_inst_4 : Group.{u1} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u1} G₁ (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u1} N₁ (MulOneClass.toMul.{u1} N₁ (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (f₂ : MonoidHom.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u1)} (MonoidHom.{u4, u1} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u1} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u1} N₁ (DivInvMonoid.toMonoid.{u1} N₁ (Group.toDivInvMonoid.{u1} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u3), succ u3, succ u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u4 u3, u3, u4} (MonoidHom.{u3, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u3} G 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G₁ _inst_5))) (MonoidHom.monoidHomClass.{u3, u2} G G₁ (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{max u3 u4, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHom.comp.{max u3 u4, max u2 u1, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (SemidirectProduct.rightHom.{u1, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.map.{u4, u3, u1, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h)) (MonoidHom.comp.{max u3 u4, u3, u2} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) G G₁ (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) f₂ (SemidirectProduct.rightHom.{u4, u3} N G _inst_1 _inst_2 φ))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.right_hom_comp_map SemidirectProduct.rightHom_comp_mapₓ'. -/
 @[simp]
 theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom :=
@@ -538,7 +538,7 @@ theorem rightHom_comp_map : rightHom.comp (map f₁ f₂ h) = f₂.comp rightHom
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} 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 but is expected to have type
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(Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ 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: N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) _inst_4)))) (MulOneClass.toMul.{max u3 u4} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max u3 u4, u4, max u3 u4} (MonoidHom.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.inl.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N) => N₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))))) f₁ n))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u2) (succ u4)} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHom.comp.{u2, u2, u4} N N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N 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: N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (MulOneClass.toMul.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) _inst_4)))) (MulOneClass.toMul.{max u3 u4} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) (MonoidHomClass.toMulHomClass.{max u3 u4, u4, max u3 u4} (MonoidHom.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁)))) (MonoidHom.monoidHomClass.{u4, max u3 u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (DivInvMonoid.toMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) (Group.toDivInvMonoid.{u4} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) _inst_4))) (Monoid.toMulOneClass.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u4 u3} (SemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁))))))) (SemidirectProduct.inl.{u4, u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) n) G₁ _inst_4 _inst_5 φ₁) (FunLike.coe.{max (succ u2) (succ u4), succ u2, succ u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N (fun (_x : N) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N) => N₁) _x) (MulHomClass.toFunLike.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))) (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHomClass.toMulHomClass.{max u2 u4, u2, u4} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (MonoidHom.monoidHomClass.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))))) f₁ n))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_inl SemidirectProduct.map_inlₓ'. -/
 @[simp]
 theorem map_inl (n : N) : map f₁ f₂ h (inl n) = inl (f₁ n) := by simp [map]
@@ -548,7 +548,7 @@ theorem map_inl (n : N) : map f₁ f₂ h (inl n) = inl (f₁ n) := by simp [map
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) (fun (_x : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ 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(MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) 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(DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inl.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u1, u3, max u3 u4} N N₁ (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ 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 but is expected to have type
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(Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u3)} (MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u3} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) 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G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} N (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u4 u1, max u3 u2} N (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) 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(SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inl.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₁)
+  forall {N : Type.{u4}} {G : Type.{u1}} [_inst_1 : Group.{u4} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u4) (succ u3)} (MonoidHom.{u4, u3} N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u4, u4, u3} N N N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u4, u4} N N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (FunLike.coe.{max (succ u4) (succ u1), succ u1, succ u4} (MonoidHom.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N 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(MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N 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(DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))) G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u4} G (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))) (MulAut.instGroupMulAut.{u4} N (MulOneClass.toMul.{u4} N (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u4, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G₁) => MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (MonoidHomClass.toMulHomClass.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u1, u2} (MonoidHom.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u2} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} N (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u4 u1, max u3 u2} N (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u4 u1} (SemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u4, u1} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u4, u1, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inl.{u4, u1} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u3, max u2 u3} N N₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} N (DivInvMonoid.toMonoid.{u4} N (Group.toDivInvMonoid.{u4} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inl.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₁)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_comp_inl SemidirectProduct.map_comp_inlₓ'. -/
 @[simp]
 theorem map_comp_inl : (map f₁ f₂ h).comp inl = inl.comp f₁ := by ext <;> simp
@@ -558,7 +558,7 @@ theorem map_comp_inl : (map f₁ f₂ h).comp inl = inl.comp f₁ := by ext <;>
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (SemidirectProduct.inr.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))
 but is expected to have type
-  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u2) (succ u4)} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHom.comp.{u2, u2, u4} N N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) 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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u4, u4} N N₁ N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) 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(Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => G₁) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} G₁ (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))))) f₂ g))
+  forall {N : Type.{u2}} {G : Type.{u1}} [_inst_1 : Group.{u2} N] [_inst_2 : Group.{u1} G] {φ : MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))} {N₁ : Type.{u4}} {G₁ : Type.{u3}} [_inst_4 : Group.{u4} N₁] [_inst_5 : Group.{u3} G₁] {φ₁ : MonoidHom.{u3, u4} G₁ (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (Monoid.toMulOneClass.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (Group.toDivInvMonoid.{u4} (MulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u4} N₁ (MulOneClass.toMul.{u4} N₁ (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (f₂ : MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u2) (succ u4)} (MonoidHom.{u2, u4} N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4)))) (MonoidHom.comp.{u2, u2, u4} N N N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u2, u2} N N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N 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(MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))) G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u1, u2} G (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (DivInvMonoid.toMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (Group.toDivInvMonoid.{u2} (MulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))) (MulAut.instGroupMulAut.{u2} N (MulOneClass.toMul.{u2} N (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u2, u4, u4} N N₁ N₁ (Monoid.toMulOneClass.{u2} N (DivInvMonoid.toMonoid.{u2} N (Group.toDivInvMonoid.{u2} N _inst_1))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) (Monoid.toMulOneClass.{u4} N₁ (DivInvMonoid.toMonoid.{u4} N₁ (Group.toDivInvMonoid.{u4} N₁ _inst_4))) 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(Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2)))) (MulOneClass.toMul.{u3} G₁ (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u1 u3, u1, u3} (MonoidHom.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u1, u3} G G₁ (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_2))) (Monoid.toMulOneClass.{u3} G₁ (DivInvMonoid.toMonoid.{u3} G₁ (Group.toDivInvMonoid.{u3} G₁ _inst_5)))))) f₂ g))
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_inr SemidirectProduct.map_inrₓ'. -/
 @[simp]
 theorem map_inr (g : G) : map f₁ f₂ h (inr g) = inr (f₂ g) := by simp [map]
@@ -568,7 +568,7 @@ theorem map_inr (g : G) : map f₁ f₂ h (inr g) = inr (f₂ g) := by simp [map
 lean 3 declaration is
   forall {N : Type.{u1}} {G : Type.{u2}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u2} G] {φ : MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u4}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u4} G₁] {φ₁ : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u3) (succ u1)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) f₁ (MulEquiv.toMonoidHom.{u1, u1} N N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u2) (succ u1)} (MonoidHom.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N 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(Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) => G -> (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))) (MonoidHom.hasCoeToFun.{u2, u1} G (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.group.{u1} N (MulOneClass.toHasMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (coeFn.{max (succ u3) (succ u4), max (succ u4) (succ u3)} (MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) (fun (_x : MonoidHom.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) => G₁ -> (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))) (MonoidHom.hasCoeToFun.{u4, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.group.{u3} N₁ (MulOneClass.toHasMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) φ₁ (coeFn.{max (succ u4) (succ u2), max (succ u2) (succ u4)} (MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) (fun (_x : MonoidHom.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) => G -> G₁) (MonoidHom.hasCoeToFun.{u2, u4} G G₁ (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5)))) f₂ g))) f₁)), Eq.{max (succ (max u3 u4)) (succ u2)} (MonoidHom.{u2, max u3 u4} G (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u2, max u1 u2, max u3 u4} G (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u2} (SemidirectProduct.{u1, u2} N G _inst_1 _inst_2 φ) (SemidirectProduct.group.{u1, u2} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u2, u3, u4} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inr.{u1, u2} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u2, u4, max u3 u4} G G₁ (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_2))) (Monoid.toMulOneClass.{u4} G₁ (DivInvMonoid.toMonoid.{u4} G₁ (Group.toDivInvMonoid.{u4} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u4} (SemidirectProduct.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.group.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u4} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
 but is expected to have type
-  forall {N : Type.{u1}} {G : Type.{u4}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u4} G] {φ : MonoidHom.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulOneClass.toMul.{u4} G (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2)))) (MulOneClass.toMul.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N 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(DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1)))))))) (MonoidHom.monoidHomClass.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))))) φ g))) (MonoidHom.comp.{u1, u3, u3} N N₁ N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (MulEquiv.toMonoidHom.{u3, u3} N₁ N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))) (FunLike.coe.{max (succ u3) (succ u2), succ u2, succ u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (fun (_x : G₁) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G₁) => MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) _x) (MulHomClass.toFunLike.{max u3 u2, u2, u3} (MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MulOneClass.toMul.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u3} 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(Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : G) => G₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u4} G (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} G (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u1 u4, max u3 u2} G (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u4, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inr.{u1, u4} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u2, max u3 u2} G G₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
+  forall {N : Type.{u1}} {G : Type.{u4}} [_inst_1 : Group.{u1} N] [_inst_2 : Group.{u4} G] {φ : MonoidHom.{u4, u1} G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))} {N₁ : Type.{u3}} {G₁ : Type.{u2}} [_inst_4 : Group.{u3} N₁] [_inst_5 : Group.{u2} G₁] {φ₁ : MonoidHom.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))} (f₁ : MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (f₂ : MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (h : forall (g : G), Eq.{max (succ u1) (succ u3)} (MonoidHom.{u1, u3} N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))) (MonoidHom.comp.{u1, u1, u3} N N N₁ (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))) 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(DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (DivInvMonoid.toMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Group.toDivInvMonoid.{u1} (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (MulAut.instGroupMulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))))))) G (MulAut.{u1} N (MulOneClass.toMul.{u1} N (Monoid.toMulOneClass.{u1} N (DivInvMonoid.toMonoid.{u1} N (Group.toDivInvMonoid.{u1} N _inst_1))))) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) 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(Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))) G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4)))))))) (MonoidHom.monoidHomClass.{u2, u3} G₁ (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (DivInvMonoid.toMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (Group.toDivInvMonoid.{u3} (MulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))) (MulAut.instGroupMulAut.{u3} N₁ (MulOneClass.toMul.{u3} N₁ (Monoid.toMulOneClass.{u3} N₁ (DivInvMonoid.toMonoid.{u3} N₁ (Group.toDivInvMonoid.{u3} N₁ _inst_4))))))))))) φ₁ (FunLike.coe.{max (succ u4) (succ u2), succ u4, succ u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G (fun (_x : G) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : G) => G₁) _x) (MulHomClass.toFunLike.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (MulOneClass.toMul.{u4} G (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2)))) (MulOneClass.toMul.{u2} G₁ (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) (MonoidHomClass.toMulHomClass.{max u4 u2, u4, u2} (MonoidHom.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))) G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (MonoidHom.monoidHomClass.{u4, u2} G G₁ (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5)))))) f₂ g))) f₁)), Eq.{max (max (succ u4) (succ u3)) (succ u2)} (MonoidHom.{u4, max u3 u2} G (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁))))) (MonoidHom.comp.{u4, max u1 u4, max u3 u2} G (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (DivInvMonoid.toMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (Group.toDivInvMonoid.{max u1 u4} (SemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ) (SemidirectProduct.instGroupSemidirectProduct.{u1, u4} N G _inst_1 _inst_2 φ)))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.map.{u1, u4, u3, u2} N G _inst_1 _inst_2 φ N₁ G₁ _inst_4 _inst_5 φ₁ f₁ f₂ h) (SemidirectProduct.inr.{u1, u4} N G _inst_1 _inst_2 φ)) (MonoidHom.comp.{u4, u2, max u3 u2} G G₁ (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Monoid.toMulOneClass.{u4} G (DivInvMonoid.toMonoid.{u4} G (Group.toDivInvMonoid.{u4} G _inst_2))) (Monoid.toMulOneClass.{u2} G₁ (DivInvMonoid.toMonoid.{u2} G₁ (Group.toDivInvMonoid.{u2} G₁ _inst_5))) (Monoid.toMulOneClass.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (DivInvMonoid.toMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (Group.toDivInvMonoid.{max u3 u2} (SemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) (SemidirectProduct.instGroupSemidirectProduct.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁)))) (SemidirectProduct.inr.{u3, u2} N₁ G₁ _inst_4 _inst_5 φ₁) f₂)
 Case conversion may be inaccurate. Consider using '#align semidirect_product.map_comp_inr SemidirectProduct.map_comp_inrₓ'. -/
 @[simp]
 theorem map_comp_inr : (map f₁ f₂ h).comp inr = inr.comp f₂ := by ext <;> simp [map]

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

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>

@@ -219,7 +219,7 @@ def lift (f₁ : N →* H) (f₂ : G →* H)
   toFun a := f₁ a.1 * f₂ a.2
   map_one' := by simp
   map_mul' a b := by
-    have := fun n g ↦ FunLike.ext_iff.1 (h n) g
+    have := fun n g ↦ DFunLike.ext_iff.1 (h n) g
     simp only [MulAut.conj_apply, MonoidHom.comp_apply, MulEquiv.coe_toMonoidHom] at this
     simp only [mul_left, mul_right, map_mul, this, mul_assoc, inv_mul_cancel_left]
 #align semidirect_product.lift SemidirectProduct.lift
@@ -242,7 +242,7 @@ theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext; simp
 
 theorem lift_unique (F : N ⋊[φ] G →* H) :
     F = lift (F.comp inl) (F.comp inr) fun _ ↦ by ext; simp [inl_aut] := by
-  rw [FunLike.ext_iff]
+  rw [DFunLike.ext_iff]
   simp only [lift, MonoidHom.comp_apply, MonoidHom.coe_mk, OneHom.coe_mk, ← map_mul,
     inl_left_mul_inr_right, forall_const]
 #align semidirect_product.lift_unique SemidirectProduct.lift_unique
@@ -269,7 +269,7 @@ def map (f₁ : N →* N₁) (f₂ : G →* G₁)
   toFun x := ⟨f₁ x.1, f₂ x.2⟩
   map_one' := by simp
   map_mul' x y := by
-    replace h := FunLike.ext_iff.1 (h x.right) y.left
+    replace h := DFunLike.ext_iff.1 (h x.right) y.left
     ext <;> simp_all
 #align semidirect_product.map SemidirectProduct.map
 

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

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

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

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathlib.Algebra.Hom.Aut
-import Mathlib.Logic.Function.Basic
+import Mathlib.Algebra.Group.Aut
 import Mathlib.GroupTheory.Subgroup.Basic
+import Mathlib.Logic.Function.Basic
 
 #align_import group_theory.semidirect_product from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"
 

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

@@ -66,8 +66,7 @@ variable {φ : G →* MulAut N}
 instance : Mul (SemidirectProduct N G φ) where
   mul a b := ⟨a.1 * φ a.2 b.1, a.2 * b.2⟩
 
-lemma mul_def (a b : SemidirectProduct N G φ) :
-  a * b = ⟨a.1 * φ a.2 b.1, a.2 * b.2⟩ := rfl
+lemma mul_def (a b : SemidirectProduct N G φ) : a * b = ⟨a.1 * φ a.2 b.1, a.2 * b.2⟩ := rfl
 
 @[simp]
 theorem mul_left (a b : N ⋊[φ] G) : (a * b).left = a.left * φ a.right b.left := rfl

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

This has nice performance benefits.

@@ -33,7 +33,7 @@ group, semidirect product
 -/
 
 
-variable (N : Type _) (G : Type _) {H : Type _} [Group N] [Group G] [Group H]
+variable (N : Type*) (G : Type*) {H : Type*} [Group N] [Group G] [Group H]
 
 /-- The semidirect product of groups `N` and `G`, given a map `φ` from `G` to the automorphism
   group of `N`. It the product of sets with the group operation
@@ -260,7 +260,7 @@ end lift
 
 section Map
 
-variable {N₁ : Type _} {G₁ : Type _} [Group N₁] [Group G₁] {φ₁ : G₁ →* MulAut N₁}
+variable {N₁ : Type*} {G₁ : Type*} [Group N₁] [Group G₁] {φ₁ : G₁ →* MulAut N₁}
 
 /-- Define a map from `N ⋊[φ] G` to `N₁ ⋊[φ₁] G₁` given maps `N →* N₁` and `G →* G₁` that
   satisfy a commutativity condition `∀ n g, f₁ (φ g n) = φ₁ (f₂ g) (f₁ n)`.  -/

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module group_theory.semidirect_product
-! leanprover-community/mathlib commit f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Hom.Aut
 import Mathlib.Logic.Function.Basic
 import Mathlib.GroupTheory.Subgroup.Basic
 
+#align_import group_theory.semidirect_product from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"
+
 /-!
 # Semidirect product
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -113,7 +113,7 @@ instance : Inhabited (N ⋊[φ] G) := ⟨1⟩
 def inl : N →* N ⋊[φ] G where
   toFun n := ⟨n, 1⟩
   map_one' := rfl
-  map_mul' := by intros ; ext <;>
+  map_mul' := by intros; ext <;>
     simp only [mul_left, map_one, MulAut.one_apply, mul_right, mul_one]
 #align semidirect_product.inl SemidirectProduct.inl
 
@@ -138,7 +138,7 @@ theorem inl_inj {n₁ n₂ : N} : (inl n₁ : N ⋊[φ] G) = inl n₂ ↔ n₁ =
 def inr : G →* N ⋊[φ] G where
   toFun g := ⟨1, g⟩
   map_one' := rfl
-  map_mul' := by intros ; ext <;> simp
+  map_mul' := by intros; ext <;> simp
 #align semidirect_product.inr SemidirectProduct.inr
 
 @[simp]
@@ -186,12 +186,12 @@ theorem rightHom_eq_right : (rightHom : N ⋊[φ] G → G) = right := rfl
 #align semidirect_product.right_hom_eq_right SemidirectProduct.rightHom_eq_right
 
 @[simp]
-theorem rightHom_comp_inl : (rightHom : N ⋊[φ] G →* G).comp inl = 1 := by ext ; simp [rightHom]
+theorem rightHom_comp_inl : (rightHom : N ⋊[φ] G →* G).comp inl = 1 := by ext; simp [rightHom]
 #align semidirect_product.right_hom_comp_inl SemidirectProduct.rightHom_comp_inl
 
 @[simp]
 theorem rightHom_comp_inr : (rightHom : N ⋊[φ] G →* G).comp inr = MonoidHom.id _ := by
-  ext ; simp [rightHom]
+  ext; simp [rightHom]
 #align semidirect_product.right_hom_comp_inr SemidirectProduct.rightHom_comp_inr
 
 @[simp]
@@ -233,7 +233,7 @@ theorem lift_inl (n : N) : lift f₁ f₂ h (inl n) = f₁ n := by simp [lift]
 #align semidirect_product.lift_inl SemidirectProduct.lift_inl
 
 @[simp]
-theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext ; simp
+theorem lift_comp_inl : (lift f₁ f₂ h).comp inl = f₁ := by ext; simp
 #align semidirect_product.lift_comp_inl SemidirectProduct.lift_comp_inl
 
 @[simp]
@@ -241,11 +241,11 @@ theorem lift_inr (g : G) : lift f₁ f₂ h (inr g) = f₂ g := by simp [lift]
 #align semidirect_product.lift_inr SemidirectProduct.lift_inr
 
 @[simp]
-theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext ; simp
+theorem lift_comp_inr : (lift f₁ f₂ h).comp inr = f₂ := by ext; simp
 #align semidirect_product.lift_comp_inr SemidirectProduct.lift_comp_inr
 
 theorem lift_unique (F : N ⋊[φ] G →* H) :
-    F = lift (F.comp inl) (F.comp inr) fun _ ↦ by ext ; simp [inl_aut] := by
+    F = lift (F.comp inl) (F.comp inr) fun _ ↦ by ext; simp [inl_aut] := by
   rw [FunLike.ext_iff]
   simp only [lift, MonoidHom.comp_apply, MonoidHom.coe_mk, OneHom.coe_mk, ← map_mul,
     inl_left_mul_inr_right, forall_const]

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

@@ -29,7 +29,7 @@ condition `∀ n g, f₁ (φ g n) = f₂ g * f₁ n * f₂ g⁻¹`
 
 ## Notation
 
-This file introduces the global notation `N ⋊[φ] G` for `semidirect_product N G φ`
+This file introduces the global notation `N ⋊[φ] G` for `SemidirectProduct N G φ`
 
 ## Tags
 group, semidirect product

Co-authored-by: Chris Hughes <33847686+ChrisHughes24@users.noreply.github.com>